The defining data and invariants of the curves are accessed through standard functions.
Returns the level of the modular curve X as an integer.
Returns the genus of the modular curve X .
Returns the type of the model for the modular curve X, presently limited to "Atkin", "Canonical", or "Classical". This is used to determine the algorithm by which parameterized isogenies are determined.
Returns a sequence of integers, of the form [N, M, P], classifying the class of the modular curve X. The integer sequence defines a congruence subgroup of PSL2(Z) defined byΓ(N, M, P) = { .((a b atop c d)) | c ≡ 0 mod N, b ≡ 0 mod P, a ≡ 1 mod M },
where M divides (LCM)(N, P). For the models presently available, this will be the sequence [N, 1, 1], where is the level of X = X0(N).