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clear;
q:=11;
Fq:=GF(q);
Fq2<i>:=ExtensionField<Fq,x|x^2+1>;
a:=0;
b:=4;
E:=EllipticCurve([Fq|a,b]);
fac:=Factorization(#E);
fac2:=Factorization(#E(Fq2));
points:=Points(E(Fq2));
points;
#points;

points1:=Points(E(Fq));
points1;
#points1;