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 nonsingular.
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 nonsingular.
 \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
