I have been googling to find out how to verify a certain element is a generator for a given elliptic curve.
Elliptic curve over Fp for a certain prime p. p = 123456 E = EllipticCurve(GF(p), [0,1,0,1,-1])
g = E(11111111,22222222)
Q. how can I check that the element g is a generator? I tried things like E.abelian_group() d = E.gens(); d and it gives me a generator that does NOT match g.
I will appreciate for any hint/help/syntax!! thanks