clear;

Fq:=GF(17);
a:=10; b:=0;
E:=EllipticCurve([Fq|a,b]);
AllRoots(Fq!-1,2);
i:=AllRoots(Fq!-1,2)[1];
P:=Random(E);
while P eq PointsAtInfinity(E)[1] do
	P:=Random(E);
end while;
P;
E![-P[1],i*P[2]];
AutomorphismGroup(E);

clear;

Fq:=GF(19);
a:=10; b:=0;
E:=EllipticCurve([Fq|a,b]);
AllRoots(Fq!-1,2);
Fq2<i>:=ExtensionField<Fq,x|x^2+1>;
AllRoots(Fq2!-1,2)[1];
P:=Random(E);
while P eq PointsAtInfinity(E)[1] do
	P:=Random(E);
end while;
P;
E(Fq2)![-P[1],i*P[2]];
AutomorphismGroup(E);
AutomorphismGroup(BaseChange(E,Fq2));

