Function: elltamagawa
Section: elliptic_curves
C-Name: elltamagawa
Prototype: G
Help: elltamagawa(E): E being an elliptic curve over a number field,
returns the global Tamagawa number of the curve.
Doc:
The object $E$ being an elliptic curve over a number field, returns the global
Tamagawa number of the curve (including the factor at infinite places).
\bprog
? e = ellinit([1, -1, 1, -3002, 63929]); \\ curve "90c6" from elldata
? elltamagawa(e)
%2 = 288
? [elllocalred(e,p)[4] | p<-[2,3,5]]
%3 = [6, 4, 6]
? vecprod(%) \\ since e.disc > 0 the factor at infinity is 2
%4 = 144
@eprog