### 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