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2018-02-21 03:38:14 +0200 asked a question Elliptic Curve and a generator?

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