Frobenius Endomorphism of Finite field Elliptic curve for elements

edit

Starting from Sage 9.8, you can simply write .frobenius_endomorphism() to construct the Frobenius endomorphism (over the .base_field() of the curve) as a "normal" isogeny which can be evaluated, composed, and so on.

With the variables from your example:

sage: pi = TestCurve.frobenius_endomorphism()
sage: pi(P)
(5*x : 6*x : 1)

Indeed the point P has no such method.

But its coordinates do.

Construct a new point whose coordinates are obtained from those of P by applying the frobenius to them:

sage: Q = TestCurve([a.frobenius() for a in P])
sage: Q
(2*x + 5 : x + 6 : 1)