clear;
q:=67;
Fq:=GF(q);
a:=4; b:=3;
E:=EllipticCurve([Fq|a,b]);
Fq2<u>:=ExtensionField<Fq,x|x^2+1>;
Fq3<v>:=ExtensionField<Fq,x|x^3+2>;
t:=TraceOfFrobenius(E);
P:=E![15,50];
pi:=FrobeniusMap(E);
pi(P) eq P;
pi(pi(P))-t*pi(P)+q*P;
P2:=E(Fq2)![2*u+16,30*u+39];
pi(pi(P2)) eq P2;
pi(pi(P2))-t*pi(P2)+q*P2;
P3:=E(Fq3)![19*v^2+49*v+8,20*v^2+66*v+21];
pi(pi(P3))-t*pi(P3)+q*P3;
