Introduction
Creation Functions
Creation of a Modular Curve ModularCurve(X,t,N) : Sch, MonStgElt, RngIntElt -> CrvMod ModularCurve(D, N) : DB, RngIntElt -> CrvMod
Creation of Points ModuliPoints(X,E) : CrvMod, CrvEll -> SeqEnum Example CrvMod_Moduli points (H109E1)
Invariants Level(X) : CrvMod -> RngIntElt Genus(X) : CrvMod -> RngIntElt ModelType(X) : CrvMod -> MonStgElt Indices(X) : CrvMod -> SeqEnum
Modular Polynomial Databases AtkinModularPolynomial(N) : RngIntElt -> RngMPolElt CanonicalModularPolynomial(N) : RngIntElt -> RngMPolElt ClassicalModularPolynomial(N) : RngIntElt -> RngMPolElt ModularCurveDatabase(t) : MonStgElt -> DB N in D: RngIntElt, DB -> BoolElt ExistsModularCurveDatabase(t) : MonStgElt -> BoolElt Example CrvMod_Modular polynomials (H109E2)
Parametrized Structures Isogeny(E,P) : CrvEll, Pt -> MapCrvEll SubgroupScheme(E,P) : CrvEll, Pt -> CrvEllSubgroup Example CrvMod_Parametrized subgroup schemes (H109E3)
Associated Structures FunctionField(X) : CrvMod -> FldFun jFunction(X) : CrvMod -> FldFunElt BaseCurve(X) : CrvMod -> CrvMod, MapSch Example CrvMod_Modular base curve (H109E4)
Automorphisms CanonicalInvolution(X) : CrvMod -> MapSch
Class Polynomials HilbertClassPolynomial(D) : RngIntElt -> RngUPolElt WeberClassPolynomial(D) : RngIntElt -> RngUPolElt, FldFunRatUElt WeberToHilbertClassPolynomial(f,D) : RngUPolElt, RngIntElt -> RngUPolElt Example CrvMod_Standard class polynomials (H109E5) ModularCurveQuotient(N,A) : RngIntElt, [RngIntElt] -> Crv
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