- Introduction
- Creation and Basic Functions
- Creating the Modular Jacobian J0(N)
- Creating the Modular Jacobians J1(N) and JH(N)
- Abelian Varieties Attached to Modular Forms
- Abelian Varieties Attached to Modular Symbols
- Creation of Abelian Subvarieties
- Creation Using a Label
- Invariants
- Conductor
- Number of Points
- Inner Twists and Complex Multiplication
- Predicates
- CanDetermineIsomorphism(A, B) : ModAbVar, ModAbVar -> BoolElt, BoolElt, MapModAbVar
- HasMultiplicityOne(A) : ModAbVar -> BoolElt
- IsAbelianVariety(A) : ModAbVar -> BoolElt
- IsAttachedToModularSymbols(A) : ModAbVar -> BoolElt
- IsAttachedToNewform(A) : ModAbVar -> BoolElt, ModAbVar, MapModAbVar
- IsIsogenous(A, B) : ModAbVar, ModAbVar -> BoolElt
- IsIsomorphic(A, B) : ModAbVar, ModAbVar -> BoolElt, MapModAbVar
- IsOnlyMotivic(A) : ModAbVar -> BoolElt
- IsQuaternionic(A) : ModAbVar -> BoolElt
- IsSelfDual(A) : ModAbVar -> BoolElt
- IsSimple(A) : ModAbVar -> BoolElt
- Example ModAbVar_Modabvar-Predicates (H145E20)
- Example ModAbVar_Modabvar-Predicates2 (H145E21)
- Example ModAbVar_Modabvar-Predicates3 (H145E22)
- Example ModAbVar_Modabvar-Predicates4 (H145E23)
- Example ModAbVar_Modabvar-Predicates5 (H145E24)
- Example ModAbVar_Modabvar-Predicates6 (H145E25)
- Example ModAbVar_Modabvar-Predicates7 (H145E26)
- Example ModAbVar_Modabvar-Predicates8 (H145E27)
- Equality and Inclusion Testing
- Modular Embedding and Parameterization
- Coercion
- Modular Symbols to Homology
- Embeddings
- Base Change
- Additional Examples
- Homology
- Homomorphisms
- Creation
- Restriction, Evaluation, and Other Manipulations
- Restriction(phi, B) : MapModAbVar, ModAbVar -> MapModAbVar
- RestrictEndomorphism(phi, B) : MapModAbVar, ModAbVar -> MapModAbVar
- RestrictEndomorphism(phi, i) : MapModAbVar, MapModAbVar -> MapModAbVar
- RestrictionToImage(phi, i) : MapModAbVar, MapModAbVar -> MapModAbVar
- Evaluate(f, phi) : RngUPolElt, MapModAbVar -> MapModAbVar
- DivideOutIntegers(phi) : MapModAbVar -> MapModAbVar, RngIntElt
- SurjectivePart(phi) : MapModAbVar -> MapModAbVar
- UniversalPropertyOfCokernel(pi, f) : MapModAbVar, MapModAbVar -> MapModAbVar
- Example ModAbVar_Morphisms-Restriction,_Evaluation,_and_Other_Manipulations (H145E53)
- Example ModAbVar_Morphisms-Restriction,_Evaluation,_and_Other_Manipulations2 (H145E54)
- Example ModAbVar_Morphisms-Restriction,_Evaluation,_and_Other_Manipulations3 (H145E55)
- Example ModAbVar_Morphisms-Restriction,_Evaluation,_and_Other_Manipulations4 (H145E56)
- Kernels
- Images
- Cokernels
- Matrix Structure
- Arithmetic
- Inverse(phi) : MapModAbVar -> MapModAbVar, RngIntElt
- phi * psi : MapModAbVar, MapModAbVar -> MapModAbVar
- a * phi : FldRatElt, MapModAbVar -> MapModAbVar
- phi * psi : MapModAbVar, AlgMatElt -> AlgMatElt
- psi * phi : AlgMatElt, MapModAbVar -> AlgMatElt
- phi ^ n : MapModAbVar, RngIntElt -> MapModAbVar
- phi + psi : MapModAbVar, MapModAbVar -> MapModAbVar
- n + phi : FldRatElt, MapModAbVar -> MapModAbVar
- phi + n : MapModAbVar, RngIntElt -> MapModAbVar
- phi + psi : MapModAbVar, AlgMatElt -> AlgMatElt
- psi + phi : AlgMatElt, MapModAbVar -> AlgMatElt
- phi - psi : MapModAbVar, MapModAbVar -> MapModAbVar
- n - phi : FldRatElt, MapModAbVar -> MapModAbVar
- phi - n : MapModAbVar, FldRatElt -> MapModAbVar
- phi - psi : MapModAbVar, AlgMatElt -> AlgMatElt
- psi - phi : AlgMatElt, MapModAbVar -> AlgMatElt
- Example ModAbVar_Morphisms-Arithmetic (H145E61)
- Polynomials
- Invariants
- Predicates
- Endomorphism Algebras and Hom Spaces
- Arithmetic of Abelian Varieties
- Decomposing and Factoring Abelian Varieties
- Building Blocks
- Orthogonal Complements
- New and Old Subvarieties and Natural Maps
- Elements of Modular Abelian Varieties
- Subgroups of Modular Abelian Varieties
- Creation
- Elements
- Arithmetic
- Quotient(A, G) : ModAbVar, ModAbVarSubGrp -> ModAbVar, MapModAbVar
- Quotient(G) : ModAbVarSubGrp -> ModAbVar, MapModAbVar, MapModAbVar
- A / G : ModAbVar, ModAbVarSubGrp -> ModAbVar, MapModAbVar, MapModAbVar
- A meet G : ModAbVar, ModAbVarSubGrp -> ModAbVarSubGrp
- G1 + G2 : ModAbVarSubGrp, ModAbVarSubGrp -> ModAbVarSubGrp
- G1 meet G2 : ModAbVarSubGrp, ModAbVarSubGrp -> ModAbVarSubGrp
- Example ModAbVar_Subgrp-Arithmetic (H145E105)
- Underlying Abelian Group and Lattice
- Invariants
- Predicates and Comparisons
- Rational Torsion Subgroups
- Hecke and Atkin-Lehner Operators
- L-series
- Complex Period Lattice
- Tamagawa Numbers and Component Groups of Neron Models
- Elliptic Curves
- Bibliography
V2.28, 13 July 2023