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Assume E is an Elliptic Curve over the field Fp, with p a known prime, for example as obtained by

p = next_prime(p)
F = GF(p)
E = EllipticCurve([F(3),F(2)])

Is there a much faster way to check that E is of composite order (the most common case) than using the obvious

not E.cardinality().is_prime()

That could speed up the search of prime-order curves.

Assume E is an Elliptic Curve over the field Fp, with p a known prime, for example as obtained by

p = next_prime(p)
F = GF(p)
E = EllipticCurve([F(3),F(2)])

Is there a much faster way to check that E is of composite order (the most common case) than using the obvious

not E.cardinality().is_prime()

That could speed up the search of prime-order curves.

Assume E is an Elliptic Curve over the field Fp, with p a known prime, for example as obtained by

p = next_prime(p)
F = GF(p)
E = EllipticCurve([F(3),F(2)])

Is there a much faster way to check that E is of composite order (the most common case) than using the obvious

not E.cardinality().is_prime()

That could speed up the search of prime-order curves.