Small Modular Curves
- Introduction
- Small Modular Curve Models
- Projection Maps
ProjectionMap(CN,N,CM,M): Crv, RngIntElt, Crv, RngIntElt → MapSchProjectionMap(CN,N,CM,M,r): Crv, RngIntElt, Crv, RngIntElt, RngIntElt → MapSchExample: Sm Mod Crvs Proj Ex
- Automorphisms
AtkinLehnerInvolution(CN,N,d): Crv, RngIntElt, RngIntElt → MapAutSchSrAutomorphism(CN,N,r,u): Crv, RngIntElt, RngIntElt, RngElt → MapAutSchExtraAutomorphism(CN,N,u): Crv, RngIntElt, RngElt → MapAutSchAutomorphismGroupOverQ(CN,N): Crv, RngIntElt → GrpAutCrvAutomorphismGroupOverCyclotomicExtension(CN,N,n): Crv, RngIntElt, RngIntElt → GrpAutCrvAutomorphismGroupOverExtension(CN,N,n,u): Crv, RngIntElt, RngIntElt, RngElt → GrpAutCrvExample: Sm Mod Crvs Auto Ex
- Cusps and Rational Points
Cusp(CN,N,d): Crv, RngIntElt, RngIntElt → AnyCuspIsSingular(N,d): RngIntElt, RngIntElt → BoolEltCuspPlaces(CN,N,d): Crv, RngIntElt, RngIntElt → SeqEnum[PlcCrvElt]NonCuspidalQRationalPoints(CN,N): Crv, RngIntElt → SeqEnumExample: Sm Mod Crvs Cusps
- Standard Functions and Forms
jInvariant(CN,N): Crv, RngIntElt → FldFunRatMEltjFunction(CN,N): Crv, RngIntElt → FldFunFracSchEltjInvariant(p,N): Pt, RngIntElt → RngEltjInvariant(p,N): PlcCrvElt, RngIntElt → RngEltjNInvariant(p,N): Pt, RngIntElt → RngEltjNInvariant(p,N): PlcCrvElt, RngIntElt → RngEltE2NForm(CN,N): Crv, RngIntElt → DiffCrvEltE4Form(CN,N): Crv, RngIntElt → FldFunFracSchElt, DiffCrvEltE6Form(CN,N): Crv, RngIntElt → FldFunFracSchElt, DiffCrvElt
- Parametrized Structures
SubgroupScheme(p,N): Pt, RngIntElt → SchGrpEll, CrvEllSubgroupScheme(p,N): PlcCrvElt, RngIntElt → SchGrpEll, CrvEllSubgroupScheme(p,N,E): Pt, RngIntElt, CrvEll → SchGrpEllSubgroupScheme(p,N,E): PlcCrvElt, RngIntElt, CrvEll → SchGrpEllIsogeny(p,N): Pt, RngIntElt → MapSchIsogeny(p,N): PlcCrvElt, RngIntElt → MapSchIsogeny(p,N,E): Pt, RngIntElt, CrvEll → MapSchIsogeny(p,N,E): PlcCrvElt, RngIntElt, CrvEll → MapSchExample: Sm Mod Crvs Prms
- Modular Generators and \(q\)-Expansions
- Extended Example
