Function: ellnonsingularmultiple
Section: elliptic_curves
C-Name: ellnonsingularmultiple
Prototype: GG
Help: ellnonsingularmultiple(E,P): given E/Q and P in E(Q), returns the pair
[R,n] where n is the least positive integer such that R = [n]P has
everywhere good reduction. More precisely, its image in a minimal model
is everywhere non-singular.
Doc: given an elliptic curve $E/\Q$ (more precisely, a model defined over $\Q$
of a curve) and a rational point $P \in E(\Q)$, returns the pair $[R,n]$,
where $n$ is the least positive integer such that $R := [n]P$ has good
reduction at every prime. More precisely, its image in a minimal model is
everywhere non-singular.
\bprog
? e = ellinit("57a1"); P = [2,-2];
? ellnonsingularmultiple(e, P)
%2 = [[1, -1], 2]
? e = ellinit("396b2"); P = [35, -198];
? [R,n] = ellnonsingularmultiple(e, P);
? n
%5 = 12
@eprog