Function: ellissupersingular
Section: elliptic_curves
C-Name: ellissupersingular
Prototype: iGDG
Help: ellissupersingular(E,{p}): return whether the elliptic curve E, defined
 over Q or a finite field, is supersingular at p or not.
Doc:
 Return 1 if the elliptic curve $E$ defined over Q or a finite field is supersingular
 at $p$, and $0$ otherwise.
 If the curve is defined over $\Q$, $p$ must be explicitly given and have good
 reduction at $p$.
 Alternatively, $E$ can be given byt its $j$-invariant in a finite field. In
 this case $p$ must be omitted.
 \bprog
 ? g = ffprimroot(ffgen(7^5))
 %1 = x^3 + 2*x^2 + 3*x + 1
 ? [g^n | n <- [1 .. 7^5 - 1], ellissupersingular(g^n)]
 %2 = [6]
 @eprog
Variant: Also available is
 \fun{int}{elljissupersingular}{GEN j} where $j$ is a $j$-invariant of a curve
 over a finite field.
