*** Warning: new stack size = 20000000 (19.073 Mbytes).
ellwp:1:x^-2 - 1/5*x^2 + 1/75*x^6 - 2/4875*x^10 + O(x^14)
ellwp:I:x^-2 - 1/5*I*x^2 - 1/75*x^6 + 2/4875*I*x^10 + O(x^14)
ellwp:z:x^-2 - 1/5*z*x^2 + 1/75*z^2*x^6 - 2/4875*z^3*x^10 + O(x^14)
ellwp:Mod(z, z^2 + 5):x^-2 + Mod(-1/5*z, z^2 + 5)*x^2 + Mod(-1/15, z^2 + 5)*
x^6 + Mod(2/975*z, z^2 + 5)*x^10 + O(x^14)
ellwp:Mod(z, z^2 + 5):x^-2 + Mod(-1/5*z, z^2 + 5)*x^2 + Mod(-1/15, z^2 + 5)*
x^6 + Mod(2/975*z, z^2 + 5)*x^10 + O(x^14)
ellwp:Mod(4, 1009):Mod(1, 1009)*x^-2 + Mod(201, 1009)*x^2 + Mod(350, 1009)*x
^6 + Mod(345, 1009)*x^10 + O(x^14)
ellwp:z:x^-2 + 807*z*x^2 + 148*z^2*x^6 + 368*z^3*x^10 + O(x^14)
ellzeta:1:x^-1 + 1/15*x^3 - 1/525*x^7 + 2/53625*x^11 + O(x^15)
ellzeta:I:x^-1 + 1/15*I*x^3 + 1/525*x^7 - 2/53625*I*x^11 + O(x^15)
ellzeta:z:x^-1 + 1/15*z*x^3 - 1/525*z^2*x^7 + 2/53625*z^3*x^11 + O(x^15)
ellzeta:Mod(z, z^2 + 5):x^-1 + Mod(1/15*z, z^2 + 5)*x^3 + Mod(1/105, z^2 + 5
)*x^7 + Mod(-2/10725*z, z^2 + 5)*x^11 + O(x^15)
ellzeta:Mod(z, z^2 + 5):x^-1 + Mod(1/15*z, z^2 + 5)*x^3 + Mod(1/105, z^2 + 5
)*x^7 + Mod(-2/10725*z, z^2 + 5)*x^11 + O(x^15)
ellzeta:Mod(4, 1009):Mod(1, 1009)*x^-1 + Mod(942, 1009)*x^3 + Mod(959, 1009)
*x^7 + Mod(519, 1009)*x^11 + O(x^15)
ellzeta:z:x^-1 + 740*z*x^3 + 123*z^2*x^7 + 150*z^3*x^11 + O(x^15)
ellsigma:1:x + 1/60*x^5 - 1/10080*x^9 - 23/259459200*x^13 + O(x^17)
ellsigma:I:x + 1/60*I*x^5 + 1/10080*x^9 + 23/259459200*I*x^13 + O(x^17)
ellsigma:z:x + 1/60*z*x^5 - 1/10080*z^2*x^9 - 23/259459200*z^3*x^13 + O(x^17
)
ellsigma:Mod(z, z^2 + 5):x + Mod(1/60*z, z^2 + 5)*x^5 + Mod(1/2016, z^2 + 5)
*x^9 + Mod(23/51891840*z, z^2 + 5)*x^13 + O(x^17)
ellsigma:Mod(z, z^2 + 5):x + Mod(1/60*z, z^2 + 5)*x^5 + Mod(1/2016, z^2 + 5)
*x^9 + Mod(23/51891840*z, z^2 + 5)*x^13 + O(x^17)
ellsigma:Mod(4, 1009):x + Mod(740, 1009)*x^5 + Mod(607, 1009)*x^9 + Mod(802,
1009)*x^13 + O(x^17)
ellsigma:z:x + 185*z*x^5 + 101*z^2*x^9 + 990*z^3*x^13 + O(x^17)
ellformalw:1:x^3 + x^7 + 2*x^11 + 5*x^15 + O(x^19)
ellformalw:I:x^3 + I*x^7 - 2*x^11 - 5*I*x^15 + O(x^19)
ellformalw:z:x^3 + z*x^7 + 2*z^2*x^11 + 5*z^3*x^15 + O(x^19)
ellformalw:Mod(z, z^2 + 5):x^3 + Mod(z, z^2 + 5)*x^7 + Mod(-10, z^2 + 5)*x^1
1 + Mod(-25*z, z^2 + 5)*x^15 + O(x^19)
ellformalw:Mod(z, z^2 + 5):x^3 + Mod(z, z^2 + 5)*x^7 + Mod(-10, z^2 + 5)*x^1
1 + Mod(-25*z, z^2 + 5)*x^15 + O(x^19)
ellformalw:Mod(4, 1009):x^3 + Mod(4, 1009)*x^7 + Mod(32, 1009)*x^11 + Mod(32
0, 1009)*x^15 + O(x^19)
ellformalw:z:x^3 + z*x^7 + 2*z^2*x^11 + 5*z^3*x^15 + O(x^19)
ellformalpoint:1:[x^-2 - x^2 - x^6 - 2*x^10 + O(x^14), -x^-3 + x + x^5 + 2*x
^9 + O(x^13)]
ellformalpoint:I:[x^-2 - I*x^2 + x^6 + 2*I*x^10 + O(x^14), -x^-3 + I*x - x^5
- 2*I*x^9 + O(x^13)]
ellformalpoint:z:[x^-2 - z*x^2 - z^2*x^6 - 2*z^3*x^10 + O(x^14), -x^-3 + z*x
+ z^2*x^5 + 2*z^3*x^9 + O(x^13)]
ellformalpoint:Mod(z, z^2 + 5):[x^-2 + Mod(-z, z^2 + 5)*x^2 + Mod(5, z^2 + 5
)*x^6 + Mod(10*z, z^2 + 5)*x^10 + O(x^14), -x^-3 + Mod(z, z^2 + 5)*x + Mod(-
5, z^2 + 5)*x^5 + Mod(-10*z, z^2 + 5)*x^9 + O(x^13)]
ellformalpoint:Mod(z, z^2 + 5):[x^-2 + Mod(-z, z^2 + 5)*x^2 + Mod(5, z^2 + 5
)*x^6 + Mod(10*z, z^2 + 5)*x^10 + O(x^14), -x^-3 + Mod(z, z^2 + 5)*x + Mod(-
5, z^2 + 5)*x^5 + Mod(-10*z, z^2 + 5)*x^9 + O(x^13)]
ellformalpoint:Mod(4, 1009):[x^-2 + Mod(1005, 1009)*x^2 + Mod(993, 1009)*x^6
+ Mod(881, 1009)*x^10 + O(x^14), -x^-3 + Mod(4, 1009)*x + Mod(16, 1009)*x^5
+ Mod(128, 1009)*x^9 + O(x^13)]
ellformalpoint:z:[x^-2 + 1008*z*x^2 + 1008*z^2*x^6 + 1007*z^3*x^10 + O(x^14)
, -x^-3 + z*x + z^2*x^5 + 2*z^3*x^9 + O(x^13)]
ellformaldifferential:1:[1 + 2*x^4 + 6*x^8 + 20*x^12 + O(x^16), x^-2 + x^2 +
3*x^6 + 10*x^10 + O(x^14)]
ellformaldifferential:I:[1 + 2*I*x^4 - 6*x^8 - 20*I*x^12 + O(x^16), x^-2 + I
*x^2 - 3*x^6 - 10*I*x^10 + O(x^14)]
ellformaldifferential:z:[1 + 2*z*x^4 + 6*z^2*x^8 + 20*z^3*x^12 + O(x^16), x^
-2 + z*x^2 + 3*z^2*x^6 + 10*z^3*x^10 + O(x^14)]
ellformaldifferential:Mod(z, z^2 + 5):[Mod(1, z^2 + 5) + Mod(2*z, z^2 + 5)*x
^4 + Mod(-30, z^2 + 5)*x^8 + Mod(-100*z, z^2 + 5)*x^12 + O(x^16), Mod(1, z^2
+ 5)*x^-2 + Mod(z, z^2 + 5)*x^2 + Mod(-15, z^2 + 5)*x^6 + Mod(-50*z, z^2 +
5)*x^10 + O(x^14)]
ellformaldifferential:Mod(z, z^2 + 5):[Mod(1, z^2 + 5) + Mod(2*z, z^2 + 5)*x
^4 + Mod(-30, z^2 + 5)*x^8 + Mod(-100*z, z^2 + 5)*x^12 + O(x^16), Mod(1, z^2
+ 5)*x^-2 + Mod(z, z^2 + 5)*x^2 + Mod(-15, z^2 + 5)*x^6 + Mod(-50*z, z^2 +
5)*x^10 + O(x^14)]
ellformaldifferential:Mod(4, 1009):[Mod(1, 1009) + Mod(8, 1009)*x^4 + Mod(96
, 1009)*x^8 + Mod(271, 1009)*x^12 + O(x^16), Mod(1, 1009)*x^-2 + Mod(4, 1009
)*x^2 + Mod(48, 1009)*x^6 + Mod(640, 1009)*x^10 + O(x^14)]
ellformaldifferential:z:[1 + 2*z*x^4 + 6*z^2*x^8 + 20*z^3*x^12 + O(x^16), x^
-2 + z*x^2 + 3*z^2*x^6 + 10*z^3*x^10 + O(x^14)]
ellformallog:1:x + 2/5*x^5 + 2/3*x^9 + 20/13*x^13 + O(x^17)
ellformallog:I:x + 2/5*I*x^5 - 2/3*x^9 - 20/13*I*x^13 + O(x^17)
ellformallog:z:x + 2/5*z*x^5 + 2/3*z^2*x^9 + 20/13*z^3*x^13 + O(x^17)
ellformallog:Mod(z, z^2 + 5):Mod(1, z^2 + 5)*x + Mod(2/5*z, z^2 + 5)*x^5 + M
od(-10/3, z^2 + 5)*x^9 + Mod(-100/13*z, z^2 + 5)*x^13 + O(x^17)
ellformallog:Mod(z, z^2 + 5):Mod(1, z^2 + 5)*x + Mod(2/5*z, z^2 + 5)*x^5 + M
od(-10/3, z^2 + 5)*x^9 + Mod(-100/13*z, z^2 + 5)*x^13 + O(x^17)
ellformallog:Mod(4, 1009):Mod(1, 1009)*x + Mod(607, 1009)*x^5 + Mod(347, 100
9)*x^9 + Mod(797, 1009)*x^13 + O(x^17)
ellformallog:z:x + 404*z*x^5 + 337*z^2*x^9 + 312*z^3*x^13 + O(x^17)
ellformalexp:1:x - 2/5*x^5 + 2/15*x^9 - 44/975*x^13 + O(x^17)
ellformalexp:I:x - 2/5*I*x^5 - 2/15*x^9 + 44/975*I*x^13 + O(x^17)
ellformalexp:z:x - 2/5*z*x^5 + 2/15*z^2*x^9 - 44/975*z^3*x^13 + O(x^17)
ellformalexp:Mod(z, z^2 + 5):x + Mod(-2/5*z, z^2 + 5)*x^5 + Mod(-2/3, z^2 +
5)*x^9 + Mod(44/195*z, z^2 + 5)*x^13 + O(x^17)
ellformalexp:Mod(z, z^2 + 5):x + Mod(-2/5*z, z^2 + 5)*x^5 + Mod(-2/3, z^2 +
5)*x^9 + Mod(44/195*z, z^2 + 5)*x^13 + O(x^17)
ellformalexp:Mod(4, 1009):x + Mod(402, 1009)*x^5 + Mod(473, 1009)*x^9 + Mod(
617, 1009)*x^13 + O(x^17)
ellformalexp:z:x + 605*z*x^5 + 471*z^2*x^9 + 120*z^3*x^13 + O(x^17)
(E)->ellisoncurve(E,[0,0]):1:1
(E)->ellisoncurve(E,[0,0]):I:1
(E)->ellisoncurve(E,[0,0]):z:1
(E)->ellisoncurve(E,[0,0]):Mod(z, z^2 + 5):1
(E)->ellisoncurve(E,[0,0]):Mod(z, z^2 + 5):1
(E)->ellisoncurve(E,[0,0]):Mod(4, 1009):1
(E)->ellisoncurve(E,[0,0]):z:1
(E)->ellordinate(E,0):1:[0]
(E)->ellordinate(E,0):I:[0]
(E)->ellordinate(E,0):z:[0]
(E)->ellordinate(E,0):Mod(z, z^2 + 5):[0]
(E)->ellordinate(E,0):Mod(z, z^2 + 5):[0]
(E)->ellordinate(E,0):Mod(4, 1009):[Mod(0, 1009)]
(E)->ellordinate(E,0):z:[0]
(E)->elldivpol(E,5):1:5*x^12 + 62*x^10 - 105*x^8 - 300*x^6 - 125*x^4 - 50*x^
2 + 1
(E)->elldivpol(E,5):I:5*x^12 + 62*I*x^10 + 105*x^8 + 300*I*x^6 - 125*x^4 - 5
0*I*x^2 - 1
(E)->elldivpol(E,5):z:5*x^12 + 62*z*x^10 - 105*z^2*x^8 - 300*z^3*x^6 - 125*z
^4*x^4 - 50*z^5*x^2 + z^6
(E)->elldivpol(E,5):Mod(z, z^2 + 5):Mod(5, z^2 + 5)*x^12 + Mod(62*z, z^2 + 5
)*x^10 + Mod(525, z^2 + 5)*x^8 + Mod(1500*z, z^2 + 5)*x^6 + Mod(-3125, z^2 +
5)*x^4 + Mod(-1250*z, z^2 + 5)*x^2 + Mod(-125, z^2 + 5)
(E)->elldivpol(E,5):Mod(z, z^2 + 5):Mod(5, z^2 + 5)*x^12 + Mod(62*z, z^2 + 5
)*x^10 + Mod(525, z^2 + 5)*x^8 + Mod(1500*z, z^2 + 5)*x^6 + Mod(-3125, z^2 +
5)*x^4 + Mod(-1250*z, z^2 + 5)*x^2 + Mod(-125, z^2 + 5)
(E)->elldivpol(E,5):Mod(4, 1009):Mod(5, 1009)*x^12 + Mod(248, 1009)*x^10 + M
od(338, 1009)*x^8 + Mod(980, 1009)*x^6 + Mod(288, 1009)*x^4 + Mod(259, 1009)
*x^2 + Mod(60, 1009)
(E)->elldivpol(E,5):z:5*x^12 + 62*z*x^10 + 904*z^2*x^8 + 709*z^3*x^6 + 884*z
^4*x^4 + (50*z^4 + 809*z^3 + 859*z^2 + 150*z + 50)*x^2 + (5*z^4 + 1008*z^3 +
1003*z^2 + 2*z + 1)
(E)->ellxn(E,3):1:[x^9 - 12*x^7 + 30*x^5 + 36*x^3 + 9*x, 9*x^8 + 36*x^6 + 30
*x^4 - 12*x^2 + 1]
(E)->ellxn(E,3):I:[x^9 - 12*I*x^7 - 30*x^5 - 36*I*x^3 + 9*x, 9*x^8 + 36*I*x^
6 - 30*x^4 + 12*I*x^2 + 1]
(E)->ellxn(E,3):z:[x^9 - 12*z*x^7 + 30*z^2*x^5 + 36*z^3*x^3 + 9*z^4*x, 9*x^8
+ 36*z*x^6 + 30*z^2*x^4 - 12*z^3*x^2 + z^4]
(E)->ellxn(E,3):Mod(z, z^2 + 5):[Mod(1, z^2 + 5)*x^9 + Mod(-12*z, z^2 + 5)*x
^7 + Mod(-150, z^2 + 5)*x^5 + Mod(-180*z, z^2 + 5)*x^3 + Mod(225, z^2 + 5)*x
, Mod(9, z^2 + 5)*x^8 + Mod(36*z, z^2 + 5)*x^6 + Mod(-150, z^2 + 5)*x^4 + Mo
d(60*z, z^2 + 5)*x^2 + Mod(25, z^2 + 5)]
(E)->ellxn(E,3):Mod(z, z^2 + 5):[Mod(1, z^2 + 5)*x^9 + Mod(-12*z, z^2 + 5)*x
^7 + Mod(-150, z^2 + 5)*x^5 + Mod(-180*z, z^2 + 5)*x^3 + Mod(225, z^2 + 5)*x
, Mod(9, z^2 + 5)*x^8 + Mod(36*z, z^2 + 5)*x^6 + Mod(-150, z^2 + 5)*x^4 + Mo
d(60*z, z^2 + 5)*x^2 + Mod(25, z^2 + 5)]
(E)->ellxn(E,3):Mod(4, 1009):[Mod(1, 1009)*x^9 + Mod(961, 1009)*x^7 + Mod(48
0, 1009)*x^5 + Mod(286, 1009)*x^3 + Mod(286, 1009)*x, Mod(9, 1009)*x^8 + Mod
(144, 1009)*x^6 + Mod(480, 1009)*x^4 + Mod(241, 1009)*x^2 + Mod(256, 1009)]
(E)->ellxn(E,3):z:[x^9 + 997*z*x^7 + 30*z^2*x^5 + 36*z^3*x^3 + 9*z^4*x, 9*x^
8 + 36*z*x^6 + 30*z^2*x^4 + 997*z^3*x^2 + z^4]
(E)->ellmul(E,[0,0],0):1:[0]
(E)->ellmul(E,[0,0],0):I:[0]
(E)->ellmul(E,[0,0],0):z:[0]
(E)->ellmul(E,[0,0],0):Mod(z, z^2 + 5):[0]
(E)->ellmul(E,[0,0],0):Mod(z, z^2 + 5):[0]
(E)->ellmul(E,[0,0],0):Mod(4, 1009):[0]
(E)->ellmul(E,[0,0],0):z:[0]
(E)->ellneg(E,[0,0]):1:[0, 0]
(E)->ellneg(E,[0,0]):I:[0, 0]
(E)->ellneg(E,[0,0]):z:[0, 0]
(E)->ellneg(E,[0,0]):Mod(z, z^2 + 5):[0, 0]
(E)->ellneg(E,[0,0]):Mod(z, z^2 + 5):[0, 0]
(E)->ellneg(E,[0,0]):Mod(4, 1009):[0, Mod(0, 1009)]
(E)->ellneg(E,[0,0]):z:[0, 0]
-1
0
152
1031:[504, 2]
2053:[1008, 2]
4099:[4196]
8209:[8291]
16411:[8280, 2]
32771:[32545]
65537:[65115]
131101:[130579]
262147:[261873]
524309:[525362]
1048583:[1048721]
2097169:[2099343]
4194319:[4190448]
8388617:[4196176, 2]
16777259:[16776451]
33554467:[33556544]
67108879:[33553348, 2]
134217757:[134207016]
268435459:[268450764]
536870923:[536886729]
1073741827:[1073696739]
2147483659:[2147445985]
4294967311:[4294892145]
8589934609:[8589800815]
17179869209:[17179907771]
34359738421:[34359891299]
68719476767:[68719109932]
137438953481:[137439150447]
274877906951:[274876963417]
549755813911:[549755723143]
1099511627791:[1099510624080]
2199023255579:[1099512197774, 2]
4398046511119:[4398049864270]
8796093022237:[8796090641581]
17592186044423:[17592179180564]
35184372088891:[35184377696395]
70368744177679:[70368735914810]
140737488355333:[140737466844674]
281474976710677:[281474967245574]
562949953421381:[562949910045019]
1125899906842679:[562949923357406, 2]
2251799813685269:[2251799812875502]
4503599627370517:[4503599672855988]
9007199254740997:[9007199395723803]
18014398509482143:[18014398460825440]
36028797018963971:[18014398463069820, 2]
72057594037928017:[36028797145369816, 2]
144115188075855881:[144115187446866113]
288230376151711813:[288230375567209858]
576460752303423619:[576460752721346915]
1152921504606847009:[1152921506693313952]
2305843009213693967:[2305843010596733829]
4611686018427388039:[4611686021547019756]
9223372036854775837:[9223372041689460430]
15
1
1
163663
121661
1
1023
494
0
1728
j
0
Mod(0, 5)
Mod(3, 5)
Mod(1, 2)*j
0
Mod(1, 3)*j
[0, D*a2, 0, D^2*a4, D^3*a6]
[a1, T*a1^2 + a2, a3, a4, T*a3^2 + a6]
[a1, a2, a3, a4, a6]
[0, -a1^2 - 4*a2, 0, 8*a3*a1 + 16*a4, -16*a3^2 - 64*a6]
[-a1, a1^2 + 5*a2, -5*a3, 10*a3*a1 + 25*a4, 25*a3^2 + 125*a6]
-8
-4
[0, 0, 0, -11737467275460978540, -17351253812244416823734891600, 0, -2347493
4550921957080, -69405015248977667294939566400, -1377681380425173666806670582
14340531600, 563398429222126969920, 14991483293779176135706946342400, -26569
379066176956739643152125596317141644100461473562624000, -882216989/131072, V
ecsmall([1]), [Vecsmall([128, -1])], [0, 0, 0, 0, 0, 0, 0, 0]]
[1/512, 0, 0, 0]
133304232
133304232
[[-8, -1792], [24, -1792]]
[[-4, -27], [12, -27]]
[[-8, -64], [24, -64]]
[[1, -11], [-3, -11]]
[[24, -3456], [-8, -3456]]
[[-8, -5184], [24, -5184]]
[[24, -93312], [24, -93312], [-3, -93312], [-3, -93312]]
[[-3, 11664], [-3, 11664], [24, 11664], [24, 11664]]
[[-3, -34992], [-3, -34992], [24, -34992], [24, -34992]]
[[1, 64], [1, 64], [-8, 64], [-8, 64]]
[[1, -15], [-4, -15], [8, -15], [-8, -15]]
[[1, -11648], [1, -11648], [-8, -11648], [-8, -11648]]
12
a
a
[5, -66, 148, 665, -15802]
[3, -15, -40, 40, -181]
[3, -15, -40, 40, -181]
[5, -70, -300, 1956, -28305]
8*x^9 + 54*x^8 + 393*x^7 + 2373*x^6 + 6993*x^5 + 15267*x^4 + 19998*x^3 + 473
4*x^2 - 25880*x - 30932
[0, 0]
[x, 1]
[x^4 - 13*x^2 - 74*x - 41, 4*x^3 + 9*x^2 + 26*x + 37]
[x^16 - 260*x^14 - 5968*x^13 - 39963*x^12 - 140444*x^11 - 195486*x^10 + 5215
64*x^9 + 5378114*x^8 + 23699984*x^7 + 74549288*x^6 + 183951360*x^5 + 3366091
54*x^4 + 444753656*x^3 + 432135644*x^2 + 255731272*x + 49749605, 16*x^15 + 1
80*x^14 + 1792*x^13 + 14753*x^12 + 84148*x^11 + 414370*x^10 + 1658348*x^9 +
4652985*x^8 + 9212312*x^7 + 10904612*x^6 + 434120*x^5 - 24648228*x^4 - 39304
176*x^3 - 13741184*x^2 + 25100064*x + 25859152]
[x^25 - 650*x^23 - 23335*x^22 - 259290*x^21 - 1456154*x^20 - 2820445*x^19 +
20761370*x^18 + 277111495*x^17 + 2007242185*x^16 + 11282671667*x^15 + 529194
54495*x^14 + 207385350880*x^13 + 677127946605*x^12 + 1857857835015*x^11 + 43
12300313262*x^10 + 8526087679330*x^9 + 14394585463670*x^8 + 20512909438825*x
^7 + 23836827014955*x^6 + 20324637565929*x^5 + 7866409553255*x^4 - 796635515
1205*x^3 - 15373355872840*x^2 - 10304273387855*x - 2425203075812, 25*x^24 +
450*x^23 + 6865*x^22 + 90410*x^21 + 848806*x^20 + 6747580*x^19 + 45352495*x^
18 + 229321140*x^17 + 838958290*x^16 + 2007441886*x^15 + 1506282910*x^14 - 1
1941908510*x^13 - 67097680775*x^12 - 197749423840*x^11 - 360107712461*x^10 -
248110872190*x^9 + 863441551840*x^8 + 3852505140470*x^7 + 8796991424540*x^6
+ 14201708642530*x^5 + 17446507273700*x^4 + 16338035413000*x^3 + 1142822256
7925*x^2 + 5633997157650*x + 1472351694025]
[0]
[-23338430276487649199700397847721116081702650343430925719105465344187224269
2167848859501069746367317057135733659821516586965453870026354744714986684965
8323996212283434950398700511439/21452304628477972409549628569820513272484339
3023834534814913254065684077308619895779034479691808535960623339165042624323
5345631919723231687684699452030828176986716708998958804636224, -892721634620
8423324340896231392069270729522715981007828685033969863523382353428674866926
4734542739355918998020644016664732197288414787069129806148688960193235312780
7158822883693587635120259554260938849967680317634128924102700969620674883736
9307779952513049787052947107461/31420343828112469950094830391399473730286380
5713026983524763427660191121031569408909200906270720147570836507805210795709
8988916304745235223129078126602318052803199405011168522054272192266092941904
104143227672460543588095008724194999641591292020853488313837016518733957632]
[-1, 1]
[-1, -3]
[833245230963211172586751702962398963656841653/30025043966406435914574252820
2802293592821136, -572865877831905829779071583256995923720966703129995025914
40045201397/5202660393781989115440421988056492168066969880055771334597510887
616]
[-10325327/6270016, -17317169781/15700120064]
[-10325327/6270016, -17317169781/15700120064]
16*x^33 + 20048*x^30 - 524864*x^27 - 20273280*x^24 - 35051520*x^21 - 1832755
20*x^18 - 818626560*x^15 - 1017937920*x^12 - 390856704*x^9 + 74973184*x^6 +
102760448*x^3 + 4194304
0
[1, 0]
[-1, -1]
[3.1096482423243803285501491221965830079, 1.55482412116219016427507456109829
15039 + 1.0643747452102737569438859937299427442*I]
[6.2192964846487606571002982443931660158, 3.10964824232438032855014912219658
30079 + 2.1287494904205475138877719874598854884*I]
[5.5614800275334595421263952543627169988, 2.78074001376672977106319762718135
84994 - 2.1374995527123861323185270948750077575*I]
[6.2192964846487606571002982443931660158, 3.10964824232438032855014912219658
30079 + 2.1287494904205475138877719874598854884*I]
[-1.1547274830668428355945002349018042438, -0.828886258466578582202749882549
09787812 + 0.52313677422798965199542236165917364573*I, -0.828886258466578582
20274988254909787812 - 0.52313677422798965199542236165917364573*I]
[10351, [1/2, -1, -2, 5/4], 1, [11, 1; 941, 1], [[1, 5, 0, 1], [1, 5, 0, 1]]
]
[10351, [1, -1, 0, -1], 1, [11, 1; 941, 1], [[1, 5, 0, 1], [1, 5, 0, 1]]]
[0, 1, [18446744073709551629, -1020847100762815391828969860044649660923, -55
340232221128654887, 25108406941546723108427206932497066002105857518694949724
756], 1]
*** at top-level: E.omega
*** ^-----
*** _.omega: incorrect type in omega [not defined over C] (t_VEC).
[9, [9], [[Mod(3, 7), Mod(5, 7)]]]
[0, 0, 0, 413748, 716503104, 0, 827496, 2866012416, -171187407504, -19859904
, -619058681856, -226311754192704000000, 97158364170048/2807086984375, Vecsm
all([1]), [Vecsmall([128, -1])], [0, 0, 0, 0, 0, 0, 0, [[2, 3]~]]]
[1/30, -13/150, -1/10, -79/500]
1
[36, [36], [[a^4 + a, a^3 + a + 1]]]
1
[3, [3], [[0, 2]]]
1
[4, [4], [[Mod(3, 5), Mod(3, 5)]]]
[3^-1 + 2 + 2*3^2 + 2*3^5 + O(3^6)]~
[1 + 2*3 + 3^2 + 2*3^3 + 3^4 + 3^5 + 2*3^6 + 3^7 + 3^8 + O(3^10), 1 + 3 + 3^
3 + 3^4 + 2*3^5 + 2*3^6 + 2*3^7 + O(3^10), 3 + 2*3^3 + 2*3^7 + O(3^8), [1 +
2*3 + 3^2 + 2*3^3 + 3^4 + 3^6 + 3^9 + O(3^10), 1 + 3 + 2*3^2 + 3^3 + 2*3^4 +
2*3^5 + 3^6 + 3^9 + O(3^10)], 2*3^2 + 3^4 + 3^5 + 3^6 + O(3^7), [[20563, 24
337, 40465, 16489, 23050], [21109, 27838, 25318, 29611, 23050], [3 + 2*3^2 +
2*3^4 + 2*3^6 + 2*3^7 + 2*3^8 + 2*3^9 + O(3^10), 3^2 + 2*3^3 + 3^4 + 3^6 +
3^7 + 2*3^8 + 2*3^9 + O(3^10), 3^4 + 2*3^5 + 2*3^6 + 2*3^8 + O(3^10), 3^8 +
2*3^9 + O(3^10)], 0]]
error("inconsistent moduli in ellinit: 3 != 5")
error("inconsistent moduli in ellinit: 3 != 5")
error("incorrect type in elliptic curve base_ring (t_VEC).")
[3^-1 + 2 + 2*3^2 + 2*3^5 + 2*3^6 + 2*3^7 + O(3^10)]~
[3^2 + 2*3^3 + 3^4 + 2*3^5 + 3^6 + 3^7 + 2*3^8 + 3^9 + 3^10 + O(3^12), 3 + 3
^2 + 3^4 + 3^5 + 2*3^6 + 2*3^7 + 2*3^8 + O(3^11), 3 + 2*3^3 + 2*3^7 + O(3^8)
, [3^-2 + 2*3^-1 + 1 + 2*3 + 3^2 + 3^4 + 3^7 + O(3^8), 3^-2 + 3^-1 + 2 + 3 +
2*3^2 + 2*3^3 + 3^4 + 3^7 + O(3^8)], 2*3^2 + 3^4 + 3^5 + 3^6 + O(3^7)]
[3^-4 + 3^-2 + O(3^0), 2*3^-6 + 2*3^-5 + 2*3^-4 + O(3^-2)]
[2 + 2^6 + O(2^9), Mod(x, x^2 + (2 + 2^2 + 2^3 + 2^4 + 2^5 + 2^7 + 2^8 + O(2
^9))), 2^3 + 2^4 + O(2^8), [2^-3 + 2^2 + 2^4 + 2^7 + 2^10 + O(2^11), 2^-3 +
2^2 + 2^5 + 2^6 + 2^10 + O(2^13)], 1, [[9377, 4065, 481], [8993, 7137, 1505]
, [2^4 + 2^5 + O(2^11), 2^7 + O(2^9)], -3]]
[1 + 2^2 + 2^7 + 2^9 + 2^11 + O(2^13), Mod(x, x^2 + (1 + 2 + 2^3 + 2^4 + 2^5
+ 2^6 + 2^8 + 2^10 + 2^12 + O(2^13))), 2^6 + 2^10 + 2^11 + O(2^12), [2^-2 +
1 + 2 + 2^4 + 2^9 + 2^10 + O(2^15), 2^-2 + 1 + 2 + 2^4 + 2^8 + 2^11 + 2^15
+ O(2^16)], 1, [[6221, 7757], [140365, 7757], [2^8 + 2^10 + 2^11 + 2^12 + 2^
13 + 2^14 + O(2^15)], -2]]
x^-2 + 31/15*x^2 + 2501/756*x^4 + 961/675*x^6 + 77531/41580*x^8 + O(x^9)
[5.0000000000000000000000000000000000000, 4.99999999999999999999999999999999
99998]
[-12.064158953746718488850195394125882872 - 15.92520450223955742328295296854
0594886*I, 176.27130319116395732662786731582177463 - 31.20263982848450159665
8857828111044055*I]
[0]
[-1.2137559863387746413172077159498331998, -0.757861263970860955134912630669
68406624*I]
[-1, -2*w]
4.9747357492884922209880132412724056589 - 3.14159265358979323846264338327950
28842*I
0.E-38 + 2.2847332495354101318966341082212062060*I
[-0.11111111111111111111110856972094952393 - 1512366075204170948725763450259
63248351/100000000000000000000000000000000000000000000000000*I, 7.3468396926
392969248046033576390354864 E-40 + 1/100000000000000000000000000000000000000
00000000000*I]
[-1, 1/2*I]
[[-1, 1/2*I], [0.59200051084078635056480901325155142952, -6.5791855625999796
522076912731847814832*I]]
[1, 1]
x^-2 - 1/5*x^2 - 1/7*x^4 + 1/75*x^6 + 3/385*x^8 + 277/238875*x^10 - 2/5775*x
^12 + O(x^14)
x^-2 - 1/5*x^2 - 1/7*x^4 + 1/75*x^6 + O(x^7)
8.9760336058655702799613054290253052730
-8.9795585687185301843619815765809019105
0.0070737179180847219897019688523688143770 - 4.54459013280902760664280136539
71181200*I
[1, 2]
x^-2 + 103.98999607107861876118376809420672237*x^2 - 649.9550420035218272005
1926719405777425*x^4 + 3604.6397609543155221247400145868915015*x^6 - 18433.3
15162997447301537872827568145124*x^8 + 90164.1927526450698484311468148077532
96*x^10 - 425973.41586156854974946172781042993149*x^12 + O(x^14)
x^-2 + 103.98999607107861876118376809420672237*x^2 - 649.9550420035218272005
1926719405777425*x^4 + 3604.6397609543155221247400145868915015*x^6 + O(x^7)
15.663727422159594482268754503777038256
-39.480069718736152480166362703315829534
11.908171148288278998948804099769395642 + 1.97957325252946376553721096563444
46755*I
[1, 3]
x^-2 + 103.98999607107861876118376809420672237*x^2 - 649.9550420035218272005
1926719405777425*x^4 + 3604.6397609543155221247400145868915015*x^6 - 18433.3
15162997447301537872827568145124*x^8 + 90164.1927526450698484311468148077532
96*x^10 - 425973.41586156854974946172781042993149*x^12 + O(x^14)
x^-2 + 103.98999607107861876118376809420672237*x^2 - 649.9550420035218272005
1926719405777425*x^4 + 3604.6397609543155221247400145868915015*x^6 + O(x^7)
15.663727422159594482268754503777038256
-39.480069718736152480166362703315829534
11.908171148288278998948804099769395642 + 1.97957325252946376553721096563444
46755*I
[2, 1]
x^-1 + 1/15*x^3 + 1/35*x^5 - 1/525*x^7 - 1/1155*x^9 - 277/2627625*x^11 + 2/7
5075*x^13 + O(x^15)
x^-1 + 1/15*x^3 + 1/35*x^5 - 1/525*x^7 + O(x^8)
3.0025857981852417376980007365038576528
-3.0023507303355942712341893343171384978*I
1.4945837634650773441141478432745008118 - 1.49552579635851441107083905597206
14467*I
[2, 2]
x^-1 - 34.663332023692872920394589364735574123*x^3 + 129.9910084007043654401
0385343881155485*x^5 - 514.94853727918793173210571636955592878*x^7 + 2048.14
61292219385890597636475075716805*x^9 - 8196.74479569500634985737698316434120
88*x^11 + 32767.185835505273057650902139263840884*x^13 + O(x^15)
x^-1 - 34.663332023692872920394589364735574123*x^3 + 129.9910084007043654401
0385343881155485*x^5 - 514.94853727918793173210571636955592878*x^7 + O(x^8)
2.0876703200272312306836757817491311900
-0.75844907585936710327841325497105198841*I
1.8018229730105461594800210664505892466 - 4.22108966565276293974646245627813
69158*I
[2, 3]
x^-1 - 34.663332023692872920394589364735574123*x^3 + 129.9910084007043654401
0385343881155485*x^5 - 514.94853727918793173210571636955592878*x^7 + 2048.14
61292219385890597636475075716805*x^9 - 8196.74479569500634985737698316434120
88*x^11 + 32767.185835505273057650902139263840884*x^13 + O(x^15)
x^-1 - 34.663332023692872920394589364735574123*x^3 + 129.9910084007043654401
0385343881155485*x^5 - 514.94853727918793173210571636955592878*x^7 + O(x^8)
2.0876703200272312306836757817491311900
-0.75844907585936710327841325497105198841*I
1.8018229730105461594800210664505892466 - 4.22108966565276293974646245627813
69158*I
[3, 1]
x + 1/60*x^5 + 1/210*x^7 - 1/10080*x^9 - 1/138600*x^11 - 167/259459200*x^13
- 19/1513512000*x^15 + O(x^17)
x + 1/60*x^5 + 1/210*x^7 - 1/10080*x^9 + O(x^10)
0.33340409272605175654322174351877926789
0.33339973807064633526799756411632693201*I
0.33307632454406929865753194192439552171 + 0.3330414840427217068846417452694
8964210*I
[3, 2]
x - 8.6658330059232182300986473411838935307*x^5 + 21.66516806678406090668397
5573135259142*x^7 - 26.820236316624371444380506060914371291*x^9 + 17.0678844
10182821575498030395896430672*x^11 + 0.9724196316598484235781214649285975622
3*x^13 - 15.440886182405758633317637416815798050*x^15 + O(x^17)
x - 8.6658330059232182300986473411838935307*x^5 + 21.66516806678406090668397
5573135259142*x^7 - 26.820236316624371444380506060914371291*x^9 + O(x^10)
0.30631122697380979289268115078987850649
0.28630802922181366479814671169863862828*I
0.53021646242894349905972369056429285872 + 0.3781418838145237834855647058271
9409288*I
[3, 3]
x - 8.6658330059232182300986473411838935307*x^5 + 21.66516806678406090668397
5573135259142*x^7 - 26.820236316624371444380506060914371291*x^9 + 17.0678844
10182821575498030395896430672*x^11 + 0.9724196316598484235781214649285975622
3*x^13 - 15.440886182405758633317637416815798050*x^15 + O(x^17)
x - 8.6658330059232182300986473411838935307*x^5 + 21.66516806678406090668397
5573135259142*x^7 - 26.820236316624371444380506060914371291*x^9 + O(x^10)
0.30631122697380979289268115078987850649
0.28630802922181366479814671169863862828*I
0.53021646242894349905972369056429285872 + 0.3781418838145237834855647058271
9409288*I
[4, 1]
0
0
-1.0984000330177788282680372407424344829
-1.0984130942966868400436474225688716324 + 1.5707963267948966192313216916397
514421*I
-0.75286232322707031868584884787482252469 + 0.785345859584418994173505759767
90041015*I
[4, 2]
0
0
-1.1831536122930622250712755356827420688
-1.2506870224867757820652851907990498543 + 1.5707963267948966192313216916397
514421*I
-0.42886850134944751864186009377385060418 + 0.619519575104929600932212172490
11490053*I
[4, 3]
0
0
-1.1831536122930622250712755356827420688
-1.2506870224867757820652851907990498543 + 1.5707963267948966192313216916397
514421*I
-0.42886850134944751864186009377385060418 + 0.619519575104929600932212172490
11490053*I
[2.5135797437238231405782694715779164652, 1.25678987186191157028913473578895
82326 + 0.78959476569186174055147277865716603189*I]
[3.1415926535897932384626433832795028842, 9.42477796076937971538793014983850
86526*I]
(x)->elleisnum(x,2)
-2.9936282668967606065680548947245432597 - 7.1637767384648910133063235008836
078048*I
157.90045350239951165298459055643475560
157.90045350239951165298459055643475560
(x)->real(elleisnum(x,4,1))
-3.9999999999999999999999999999999999999
2079.7999214215723752236753618841344474
2079.7999214215723752236753618841344474
(x)->real(elleisnum(x,6,1))
-4.0000000000000000000000000000000000000
-18198.741176098611161614539481433617679
-18198.741176098611161614539481433617679
(x)->real(elleisnum(x,10))
-41471.999999999999999999999999999999999
98106527293.111533926136928277796284706
98106527293.111533926136928277796284706
45515516542954982422.225456145489798060
2.0716622535417196510500376518804560198 E39
-1
[0]
347813742467679407541/38941611811810745401
[0.49999999999999999999999999999999999984 + 0.999999999999999999999999999999
99999995*I, 1.5617041082089070087003342842479112065 + 0.56028539298876740518
391807553710802963*I]
*** at top-level: ellpointtoz(e,[Mod(3,'x^2+1),1])
*** ^--------------------------------
*** ellpointtoz: incorrect type in ellpointtoz (t_VEC).
3 + 11^2 + 2*11^3 + 3*11^4 + 6*11^5 + 10*11^6 + 8*11^7 + O(11^8)
O(11^8)
Mod((2 + 2*3 + 2*3^2 + 2*3^3 + 2*3^4 + 2*3^5 + 2*3^6 + 2*3^7 + 2*3^8 + O(3^9
)), x^2 + (1 + 3 + 2*3^4 + 3^8 + O(3^9)))
Mod(O(3^9), x^2 + (1 + 3 + 2*3^4 + 3^8 + O(3^9)))
*** at top-level: testzellQp(e,ellmul(e,[0,0],2))
*** ^-------------------------------
*** in function testzellQp: my(a,q,Q);a=ellpointtoz(e,P);Q=ellztopoint(e,a
*** ^----------------------------------
*** ellpointtoz: sorry, ellpointtoz when u not in Qp is not yet implemented.
Mod((2 + 2*3 + 3^2 + 3^3 + 3^5 + 3^7 + O(3^10))*x + (1 + 3 + 2*3^2 + 2*3^4 +
2*3^5 + 3^6 + 3^8 + 2*3^9 + O(3^10)), x^2 + (3 + 3^3 + 2*3^4 + 3^5 + 2*3^6
+ 3^7 + 2*3^8 + 3^9 + 2*3^10 + 3^11 + O(3^13)))
Mod(O(3^10)*x + O(3^10), x^2 + (3 + 3^3 + 2*3^4 + 3^5 + 2*3^6 + 3^7 + 2*3^8
+ 3^9 + 2*3^10 + 3^11 + O(3^13)))
Mod((2^2 + 2^4 + 2^5 + 2^6 + 2^8 + O(2^10))*x + (1 + 2 + 2^2 + 2^8 + O(2^11)
), x^2 + (1 + 2^2 + 2^4 + 2^5 + 2^7 + 2^8 + 2^9 + O(2^11)))
Mod(O(2^11)*x + O(2^9), x^2 + (1 + 2^2 + 2^4 + 2^5 + 2^7 + 2^8 + 2^9 + O(2^1
1)))
4*5 + 3*5^2 + 2*5^4 + 2*5^5 + 3*5^6 + 3*5^7 + 3*5^8 + 3*5^9 + 3*5^10 + O(5^1
1)
O(5^10)
2 + O(2^8)
O(2^9)
2^7 + 2^8 + 2^10 + 2^11 + 2^13 + 2^15 + O(2^18)
O(2^15)
[Mod(0, 11), Mod(0, 11), Mod(0, 11), Mod(1, 11), Mod(1, 11), Mod(0, 11), Mod
(2, 11), Mod(4, 11), Mod(10, 11), Mod(7, 11), Mod(5, 11), Mod(10, 11), Mod(9
, 11), Vecsmall([3]), [11, [9, 5, [6, 0, 0, 0]]], [0, 0, 0, 0]]
1
[0.86602540378443864676372317075293618347 - 1/2*I, -0.8660254037844386467637
2317075293618348 - 1/2*I]
[-2, 3]
[0, 1]
[1, 0, 0, 0]
0.035247504442186170440172838583518049039
*** at top-level: ellheight(E,[0.,0])
*** ^-------------------
*** ellheight: incorrect type in ellheight [not a rational point] (t_VEC).
[1, 0, 0, 0]
[100000000000000000039, 0, 0, 0]
[0, 0, 0, 1, 1, 0, 2, 4, -1, -48, -864, -496, 6912/31, Vecsmall([1]), [Vecsm
all([128, -1])], [0, 0, 0, 0, 0, 0, 0, [[2]~]]]
[0, 0, 0, 1/16, 1/64, 0, 1/8, 1/16, -1/256, -3, -27/2, -31/256, 6912/31, Vec
small([1]), [Vecsmall([128, -1])], [0, 0, 0, 0, 0, 0, 0, [[2]~, [1/2, 0, 0,
0], [0, 0, 0, 1, 1, 0, 2, 4, -1, -48, -864, -496, 6912/31, Vecsmall([1]), [V
ecsmall([128, -1])], [0, 0, 0, 0, 0, 0, 0, [[2]~]]]]]]
0
20 0 0 -16 0 -4 14 8 0 0 0 26 0 2 0 -28
11124672632 0 0 0 0 0 9623756642 1757839784 0 10364773916 0 -11268052540 -89
20565254 10819287710 0 0 0 8122434446
1728
0 0 -22 0 -14 0 -22 0 0 26 0 18 0 -14 2 0
0 -11632185758 0 11654847458 0 6266694946 12139026234 0 -765697030 0 -993589
2958 0 11860023378 -8888351742 0 -12108381446 0 -12120201878
-3375
16 0 -10 0 -22 24 0 -20 0 0 4 0 8 -18 -26 0
3823447300 13247194 -10908503128 0 1880681120 0 0 12050551284 10977324518 0
0 0 -948699894 0 0 9979357082 11495943932 0
8000
0 -18 6 22 0 0 0 2 0 0 18 0 0 22 0 0
-10793410270 0 0 30 0 0 0 2640064994 8901937002 0 0 0 0 8077589434 0 5325840
630 -5129549082 0
54000
20 0 0 16 0 4 -14 -8 0 0 0 26 0 2 0 -28
-11124672632 0 0 0 0 0 -9623756642 1757839784 0 10364773916 0 -11268052540 8
920565254 -10819287710 0 0 0 8122434446
-32768
0 0 3 0 0 0 23 16 0 0 21 25 -15 0 0 -20
7894594559 0 0 9919498893 0 0 -7887871151 0 0 0 0 0 491192422 -8259190543 0
0 0 12121352347
287496
0 0 22 0 -14 0 22 0 0 -26 0 -18 0 14 2 0
0 -11632185758 0 11654847458 0 -6266694946 -12139026234 0 -765697030 0 99358
92958 0 11860023378 8888351742 0 -12108381446 0 12120201878
-884736
0 7 23 -9 11 0 18 -24 0 0 0 0 17 0 -22 -25
0 -8412576737 0 0 0 0 8538343901 12113814432 -11651750401 12092421657 0 0 0
0 0 -11058211849 0 -1330007630
-12288000
20 0 0 -23 0 19 14 25 0 0 0 7 0 23 0 -11
-9788647777 0 0 0 0 0 11231998687 11288673199 0 304785419 0 -11268052540 268
1012851 10819287710 0 0 0 -11884260649
16581375
16 0 10 0 22 24 0 -20 0 0 -4 0 8 -18 -26 0
-3823447300 13247194 -10908503128 0 1880681120 0 0 12050551284 10977324518 0
0 0 948699894 0 0 9979357082 11495943932 0
-884736000
11 0 0 -13 0 0 0 0 -25 -2 0 -6 0 -27 -10 0
-12128231367 0 -9395300833 -435256334 0 0 0 -11932204400 -10588952138 0 0 0
0 0 0 -7319300662 0 0
-147197952000
-21 -16 0 0 -23 1 5 7 20 -25 0 11 0 13 0 -27
0 11781526319 1637387588 0 12146798315 0 -8198706882 0 3977562293 8890885111
-9549303299 -11553067388 9924967665 3852111021 0 5199002617 772472488 0
-262537412640768000
0 19 0 0 0 -21 0 0 4 -23 8 0 0 0 -25 -12
0 0 6564371741 0 0 2618909413 0 2136229176 0 0 0 4357107277 1635802689 30896
18289 0 -5064045658 0 0
4294985035
[0, 1, [5, 0, 0, 0], 1]
1
0
[6.2500000000000000000000000000000000000, -140.62500000000000000000000000000
000000]
error("incorrect type in checkell (t_VEC).")
[0, 0, 0, x^2, x, 0, 2*x^2, 4*x, -x^4, -48*x^2, -864*x, -64*x^6 - 432*x^2, -
6912*x^4/(-4*x^4 - 27), Vecsmall([0]), [Vecsmall([128, 0])], [0, 0, 0, 0]]
*** at top-level: ellminimalmodel(E)
*** ^------------------
*** ellminimalmodel: incorrect type in ellminimalmodel (E / number field) (t_VEC).
*** at top-level: ellweilpairing(E,[0],[0],1)
*** ^---------------------------
*** ellweilpairing: incorrect type in checkell over Fq (t_VEC).
*** at top-level: ellinit([1])
*** ^------------
*** ellinit: incorrect type in ellxxx [not an elliptic curve (ell5)] (t_VEC).
*** at top-level: ellinit([1,1],quadgen(5))
*** ^-------------------------
*** ellinit: incorrect type in elliptic curve base_ring (t_QUAD).
*** at top-level: ellinit([Mod(1,2),1],O(2))
*** ^--------------------------
*** ellinit: incorrect type in elliptic curve base_ring (t_VEC).
*** at top-level: ellinit([O(2),1],ffgen(2^3))
*** ^----------------------------
*** ellinit: incorrect type in elliptic curve base_ring (t_VEC).
*** at top-level: ellinit([O(2),1],1.)
*** ^--------------------
*** ellinit: incorrect type in elliptic curve base_ring (t_VEC).
[0, 0, 0, 1, 2, 0, 2, 8, -1, -48, -1728, -1792, 432/7, Vecsmall([0]), [Vecsm
all([128, -1])], [0, 0, 0, 0]]
[0, 0, 0, 0, 1, 0, 0, 4, 0, 0, 1, 3, 0, Vecsmall([4]), [0, [Vecsmall([0]), V
ecsmall([0, 1]), [Vecsmall([0, 1]), Vecsmall([0]), Vecsmall([0]), Vecsmall([
0])]]], [0, 0, 0, 0]]
*** at top-level: ellinit([ffgen(5),1],3)
*** ^-----------------------
*** ellinit: inconsistent moduli in ellinit: 3 != 5
[0, 0, 0, 1.0000000000000000000000000000000000000, 1, 0, 2.00000000000000000
00000000000000000000, 4, -1.0000000000000000000000000000000000000, -48.00000
0000000000000000000000000000000, -864, -496.00000000000000000000000000000000
000, 222.96774193548387096774193548387096774, Vecsmall([0]), [Vecsmall([128,
-1])], [0, 0, 0, 0]]
*** at top-level: ellinit([1.,Mod(1,3)])
*** ^----------------------
*** ellinit: incorrect type in elliptic curve base_ring (t_VEC).
1
-1
1
1
2170814464
4
5.5851222210291762172101660392028515730
-21952
6
0.33022365934448053902826194612283487754
3.5069511370460869021391160508020304780
-52760
-52832
[[1, -1], 2]
[[509051665/47782462464, -2265512629515497/10444864034930688], 12]
ellformalw
t^3 - t^5 + t^6 - t^7 - 3*t^8 + 9*t^9 - 2*t^10 - 21*t^11 + 45*t^12 - 21*t^13
- 140*t^14 + 339*t^15 - 91*t^16 - 1051*t^17 + 2394*t^18 + O(t^19)
x^3 - x^5 + x^6 - x^7 + O(x^8)
t^3 - t^5 + t^6 - t^7 + O(t^8)
ellformalpoint
[t^-2 + 1 - t + 2*t^2 + t^3 - 5*t^4 + 3*t^5 + 5*t^6 - 19*t^7 + 22*t^8 + 33*t
^9 - 129*t^10 + 111*t^11 + 228*t^12 - 855*t^13 + O(t^14), -t^-3 - t^-1 + 1 -
2*t - t^2 + 5*t^3 - 3*t^4 - 5*t^5 + 19*t^6 - 22*t^7 - 33*t^8 + 129*t^9 - 11
1*t^10 - 228*t^11 + 855*t^12 + O(t^13)]
[x^-2 + 1 - x + 2*x^2 + O(x^3), -x^-3 - x^-1 + 1 - 2*x + O(x^2)]
[t^-2 + 1 - t + 2*t^2 + O(t^3), -t^-3 - t^-1 + 1 - 2*t + O(t^2)]
ellformaldifferential
[1 - t^2 + 2*t^3 - 3*t^4 - 6*t^5 + 23*t^6 - 12*t^7 - 53*t^8 + 160*t^9 - 131*
t^10 - 470*t^11 + 1471*t^12 - 882*t^13 - 4257*t^14 + 12628*t^15 + O(t^16), t
^-2 + t - 2*t^2 - 2*t^3 + 11*t^4 - 9*t^5 - 18*t^6 + 78*t^7 - 94*t^8 - 175*t^
9 + 725*t^10 - 676*t^11 - 1603*t^12 + 6293*t^13 + O(t^14)]
[1 - x^2 + 2*x^3 - 3*x^4 + O(x^5), x^-2 + x - 2*x^2 + O(x^3)]
[1 - t^2 + 2*t^3 - 3*t^4 + O(t^5), t^-2 + t - 2*t^2 + O(t^3)]
ellformallog
t - 1/3*t^3 + 1/2*t^4 - 3/5*t^5 - t^6 + 23/7*t^7 - 3/2*t^8 - 53/9*t^9 + 16*t
^10 - 131/11*t^11 - 235/6*t^12 + 1471/13*t^13 - 63*t^14 - 1419/5*t^15 + 3157
/4*t^16 + O(t^17)
x - 1/3*x^3 + 1/2*x^4 - 3/5*x^5 + O(x^6)
t - 1/3*t^3 + 1/2*t^4 - 3/5*t^5 + O(t^6)
ellformalexp
t + 1/3*t^3 - 1/2*t^4 + 14/15*t^5 - 1/6*t^6 - 76/315*t^7 - 7/10*t^8 + 7547/1
1340*t^9 + 977/3780*t^10 - 5116/22275*t^11 - 78977/113400*t^12 + 3069607/608
1075*t^13 + 1651/2970*t^14 - 526660427/2554051500*t^15 - 5754943993/68108040
00*t^16 + O(t^17)
x + 1/3*x^3 - 1/2*x^4 + 14/15*x^5 + O(x^6)
t + 1/3*t^3 - 1/2*t^4 + 14/15*t^5 + O(t^6)
*** at top-level: ellformalw(e,0)
*** ^---------------
*** ellformalw: domain error in ellformalw: precision <= 0
*** at top-level: ellformalw(e,-1)
*** ^----------------
*** ellformalw: domain error in ellformalw: precision <= 0
242.47010035195076100129810400142304776
0
[-0.52751724240790530394437835702346995884*I, -0.090507650025885335533571758
708283389896*I]
2
Total time spent: 548