In order to find the order of the base point on a curve, one can do something like this if the curve is in the Wiestrass form :
a = 1
b = 3141592653589793238462643383279502884197169399375105820974944592307816406665
p = 2^251 + 17*2^192 +1
E = EllipticCurve(GF(p), [0,0,0,a,b])
print(E)
print(E.abelian_group())
card = E.cardinality()
print("cardinality =",card)
factor(card)
G = E(874739451078007766457464989774322083649278607533249481151382481072868806602,152666792071518830868575557812948353041420400780739481342941381225525861407)
print("Generator order q=", G.order()) a = 1
b = 3141592653589793238462643383279502884197169399375105820974944592307816406665
p = 2^251 + 17*2^192 +1
E = EllipticCurve(GF(p), [0,0,0,a,b])
print(E)
print(E.abelian_group())
card = E.cardinality()
print("cardinality =",card)
factor(card)
G = E(874739451078007766457464989774322083649278607533249481151382481072868806602,152666792071518830868575557812948353041420400780739481342941381225525861407)
print("Generator order q=", G.order())
But how to do the same for a curve in the twisted Edwards form ? Because I suppose converting the curve and the point to the Wiestrass form would change the resulting order being computed right ?
