> iload "ex1-1.m";
Interactive-loading "ex1-1.m"
> //Define the finite field
> F := FiniteField(431);
> E:= EllipticCurve([F!1, F!0]);
> //Compute the j-invariant
> jInvariant(E);
4
> // Compute elliptic curves from j-invariant
> j := F!234;
> E1 := EllipticCurveWithjInvariant(j);
> //Check supersingularity
> IsSupersingular(E1);
true
> //Find another non-isomorphic curve with the same j-invariant
> _, E2 := Explode(QuadraticTwists(E1)); E1, E2;
Elliptic Curve defined by y^2 + x*y = x^3 + 161*x + 208 over GF(431)
Elliptic Curve defined by y^2 = x^3 + 159*x + 289 over GF(431)
> //Check whether they're isomorphic
> IsIsomorphic(E1, E2);
false
> // This is how you base change in general
> F2:= FiniteField(431^2);
> IsIsomorphic(BaseChange(E1,F2 ), BaseChange(E2, F2));
true
>
>
>