Small Modular Curve Models
SmallModularCurve(N) : RngIntElt -> Crv
IsInSmallModularCurveDatabase(N) : RngIntElt -> Boolelt
Example SmallModCrv_sm_mod_crvs_basic_ex (H129E1)
Projection Maps
ProjectionMap(CN,N,CM,M) : Crv, RngIntElt, Crv, RngIntElt -> MapSch
ProjectionMap(CN,N,CM,M,r) : Crv, RngIntElt, Crv, RngIntElt, RngIntElt -> MapSch
Example SmallModCrv_sm_mod_crvs_proj_ex (H129E2)
Automorphisms
AtkinLehnerInvolution(CN,N,d) : Crv, RngIntElt, RngIntElt -> MapAutSch
SrAutomorphism(CN,N,r,u): Crv, RngIntElt, RngIntElt, RngElt -> MapAutSch
ExtraAutomorphism(CN,N,u): Crv, RngIntElt, RngElt -> MapAutSch
AutomorphismGroupOverQ(CN,N): Crv, RngIntElt -> GrpAutCrv
AutomorphismGroupOverCyclotomicExtension(CN,N,n): Crv, RngIntElt, RngIntElt -> GrpAutCrv
AutomorphismGroupOverExtension(CN,N,n,u): Crv, RngIntElt, RngIntElt, RngElt -> GrpAutCrv
Example SmallModCrv_sm_mod_crvs_auto_ex (H129E3)
Cusps and Rational Points
Cusp(CN,N,d) : Crv, RngIntElt, RngIntElt -> Any
CuspIsSingular(N,d) : RngIntElt, RngIntElt -> BoolElt
CuspPlaces(CN,N,d) : Crv, RngIntElt, RngIntElt -> SeqEnum[PlcCrvElt]
NonCuspidalQRationalPoints(CN,N) : Crv, RngIntElt -> SeqEnum
Example SmallModCrv_sm_mod_crvs_cusps (H129E4)
Standard Functions and Forms
jInvariant(CN,N) : Crv, RngIntElt -> FldFunRatMElt
jInvariant(p,N) : Pt, RngIntElt -> RngElt
jNInvariant(p,N) : Pt, RngIntElt -> RngElt
E2NForm(CN,N) : Crv, RngIntElt -> DiffCrvElt
E4Form(CN,N) : Crv, RngIntElt -> FldFunFracSchElt, DiffCrvElt
E6Form(CN,N) : Crv, RngIntElt -> FldFunFracSchElt, DiffCrvElt
Parametrized Structures
SubgroupScheme(p,N) : Pt, RngIntElt -> SchGrpEll, CrvEll
Isogeny(p,N) : Pt, RngIntElt -> MapSch
Example SmallModCrv_sm_mod_crvs_prms (H129E5)
Modular Generators and q-Expansions
qExpansionExpressions(N) : RngIntElt ->
qExpansionsOfGenerators(N,R,r) : RngIntElt, RngSerLaur, RngIntElt -> SeqEnum
Example SmallModCrv_q_exps_ex_sm_mod_crvs (H129E6)
Extended Example
Example SmallModCrv_big_ex (H129E7)
Bibliography
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Wed Apr 24 15:09:57 EST 2013