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 (H89E1)
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 (H89E2)
Parametrized Structures
Isogeny(E,P) : CrvEll, Pt) -> MapCrvEll
SubgroupScheme(E,P) : CrvEll, Pt -> CrvEllSubgroup
Example CrvMod_Parametrized subgroup schemes (H89E3)
Associated Structures
FunctionField(X) : CrvMod -> FldFun
jFunction(X) : CrvMod -> FldFunElt
BaseCurve(X) : CrvMod -> CrvMod, MapSch
Example CrvMod_Modular base curve (H89E4)
Automorphisms
CanonicalInvolution(X) : CrvMod -> MapSch
Class Polynomials
HilbertClassPolynomial(D) : RngIntElt -> RngUPolElt
WeberClassPolynomial(D) : RngIntElt -> RngUPolElt