\BOOKMARK [1][-]{section.1}{Introduction}{}% 1
\BOOKMARK [2][-]{subsection.1.1}{`39`42`"613A``45`47`"603AGL2-type and Modular Abelian Varieties}{section.1}% 2
\BOOKMARK [2][-]{subsection.1.2}{Explicit Defining Data for Modular Abelian Varieties}{section.1}% 3
\BOOKMARK [2][-]{subsection.1.3}{Contents}{section.1}% 4
\BOOKMARK [1][-]{section.2}{Computing with Modular Abelian Varieties}{}% 5
\BOOKMARK [2][-]{subsection.2.1}{Ambient Modular Abelian Varieties}{section.2}% 6
\BOOKMARK [2][-]{subsection.2.2}{Enumerating New Simple Modular Abelian Varieties}{section.2}% 7
\BOOKMARK [2][-]{subsection.2.3}{Decomposition}{section.2}% 8
\BOOKMARK [3][-]{subsubsection.2.3.1}{New and Old Subvarieties and Quotients}{subsection.2.3}% 9
\BOOKMARK [3][-]{subsubsection.2.3.2}{Decomposition as a Product of Simples}{subsection.2.3}% 10
\BOOKMARK [3][-]{subsubsection.2.3.3}{Verifying Defining Data of a Modular Abelian Variety}{subsection.2.3}% 11
\BOOKMARK [2][-]{subsection.2.4}{Arithmetic with Modular Abelian Varieties}{section.2}% 12
\BOOKMARK [3][-]{subsubsection.2.4.1}{Sums and Products}{subsection.2.4}% 13
\BOOKMARK [3][-]{subsubsection.2.4.2}{Intersection}{subsection.2.4}% 14
\BOOKMARK [3][-]{subsubsection.2.4.3}{Complements \(Poincare Reducibility\)}{subsection.2.4}% 15
\BOOKMARK [3][-]{subsubsection.2.4.4}{Quotients by Subgroups and Subvarieties}{subsection.2.4}% 16
\BOOKMARK [2][-]{subsection.2.5}{Finite Subgroups}{section.2}% 17
\BOOKMARK [3][-]{subsubsection.2.5.1}{Defining Data}{subsection.2.5}% 18
\BOOKMARK [3][-]{subsubsection.2.5.2}{The n-Torsion Subgroup}{subsection.2.5}% 19
\BOOKMARK [3][-]{subsubsection.2.5.3}{Intersection of Finite Subgroups}{subsection.2.5}% 20
\BOOKMARK [3][-]{subsubsection.2.5.4}{The Cuspidal Subgroup}{subsection.2.5}% 21
\BOOKMARK [3][-]{subsubsection.2.5.5}{The Rational Cuspidal Subgroup}{subsection.2.5}% 22
\BOOKMARK [3][-]{subsubsection.2.5.6}{The Torsion Subgroup}{subsection.2.5}% 23
\BOOKMARK [3][-]{subsubsection.2.5.7}{The Shimura Subgroup}{subsection.2.5}% 24
\BOOKMARK [2][-]{subsection.2.6}{Morphisms Between Modular Abelian Varieties}{section.2}% 25
\BOOKMARK [3][-]{subsubsection.2.6.1}{Defining Data for Morphisms}{subsection.2.6}% 26
\BOOKMARK [3][-]{subsubsection.2.6.2}{Natural Maps}{subsection.2.6}% 27
\BOOKMARK [3][-]{subsubsection.2.6.3}{Morphisms Defined by Finite Subgroups}{subsection.2.6}% 28
\BOOKMARK [3][-]{subsubsection.2.6.4}{Kernels of Morphisms}{subsection.2.6}% 29
\BOOKMARK [3][-]{subsubsection.2.6.5}{Images of Morphisms}{subsection.2.6}% 30
\BOOKMARK [3][-]{subsubsection.2.6.6}{The Universal Property of the Cokernel}{subsection.2.6}% 31
\BOOKMARK [3][-]{subsubsection.2.6.7}{The Projection Morphism}{subsection.2.6}% 32
\BOOKMARK [3][-]{subsubsection.2.6.8}{Left and Right Inverses}{subsection.2.6}% 33
\BOOKMARK [2][-]{subsection.2.7}{Endomorphism Rings and Hom Spaces}{section.2}% 34
\BOOKMARK [3][-]{subsubsection.2.7.1}{Computing End and Hom}{subsection.2.7}% 35
\BOOKMARK [3][-]{subsubsection.2.7.2}{Computing Discriminants of Endomorphism Rings}{subsection.2.7}% 36
\BOOKMARK [3][-]{subsubsection.2.7.3}{The Hecke Subring}{subsection.2.7}% 37
\BOOKMARK [3][-]{subsubsection.2.7.4}{Atkin-Lehner Operators}{subsection.2.7}% 38
\BOOKMARK [3][-]{subsubsection.2.7.5}{The I-torsion Subgroup for any Ideal I}{subsection.2.7}% 39
\BOOKMARK [2][-]{subsection.2.8}{Isogenies and Isomorphisms of Modular Abelian Varieties}{section.2}% 40
\BOOKMARK [3][-]{subsubsection.2.8.1}{Isogenies From A to B}{subsection.2.8}% 41
\BOOKMARK [3][-]{subsubsection.2.8.2}{Isomorphisms from A to B}{subsection.2.8}% 42
\BOOKMARK [3][-]{subsubsection.2.8.3}{The Minimal Isogeny}{subsection.2.8}% 43
\BOOKMARK [2][-]{subsection.2.9}{Complex Periods}{section.2}% 44
\BOOKMARK [3][-]{subsubsection.2.9.1}{The Period Lattice}{subsection.2.9}% 45
\BOOKMARK [3][-]{subsubsection.2.9.2}{The BSD Real Volume}{subsection.2.9}% 46
\BOOKMARK [2][-]{subsection.2.10}{Component Groups}{section.2}% 47
\BOOKMARK [3][-]{subsubsection.2.10.1}{Supersingular Curves}{subsection.2.10}% 48
\BOOKMARK [3][-]{subsubsection.2.10.2}{Definite Quaternion Algebras}{subsection.2.10}% 49
\BOOKMARK [3][-]{subsubsection.2.10.3}{The Component Group}{subsection.2.10}% 50
\BOOKMARK [3][-]{subsubsection.2.10.4}{Tamagawa Numbers}{subsection.2.10}% 51
\BOOKMARK [3][-]{subsubsection.2.10.5}{J1\(N\)}{subsection.2.10}% 52
\BOOKMARK [2][-]{subsection.2.11}{Complex L-Series}{section.2}% 53
\BOOKMARK [3][-]{subsubsection.2.11.1}{Local L-factors}{subsection.2.11}% 54
\BOOKMARK [3][-]{subsubsection.2.11.2}{Numerical Evaluation at any Point}{subsection.2.11}% 55
\BOOKMARK [3][-]{subsubsection.2.11.3}{The Rational Part of the Special Value}{subsection.2.11}% 56
\BOOKMARK [3][-]{subsubsection.2.11.4}{Order of Vanishing \(Analytic Rank\)}{subsection.2.11}% 57
\BOOKMARK [3][-]{subsubsection.2.11.5}{Zeros in the Critical Strip}{subsection.2.11}% 58
\BOOKMARK [2][-]{subsection.2.12}{p-adic L-Series}{section.2}% 59
\BOOKMARK [3][-]{subsubsection.2.12.1}{The Definition}{subsection.2.12}% 60
\BOOKMARK [3][-]{subsubsection.2.12.2}{Computing to Given Precision}{subsection.2.12}% 61
\BOOKMARK [3][-]{subsubsection.2.12.3}{Computing the Leading Coefficient and Order of Vanishing}{subsection.2.12}% 62
\BOOKMARK [1][-]{section.3}{Computing the Isogeny Class}{}% 63
\BOOKMARK [2][-]{subsection.3.1}{The Class Group \205 Noneisenstein Isogenies}{section.3}% 64
\BOOKMARK [2][-]{subsection.3.2}{Eisenstein Isogenies}{section.3}% 65
\BOOKMARK [2][-]{subsection.3.3}{Enumerating the Isogeny Class}{section.3}% 66
\BOOKMARK [1][-]{section.4}{Tables of Modular Abelian Varieties}{}% 67
\BOOKMARK [2][-]{subsection.4.1}{Contents}{section.4}% 68
\BOOKMARK [2][-]{subsection.4.2}{Factors of J0\(N\) for N125}{section.4}% 69
\BOOKMARK [2][-]{subsection.4.3}{Factors of JH\(N\) for N49}{section.4}% 70
\BOOKMARK [2][-]{subsection.4.4}{Minimal Isogenies}{section.4}% 71
\BOOKMARK [2][-]{subsection.4.5}{Birch and Swinnerton-Dyer}{section.4}% 72
\BOOKMARK [2][-]{subsection.4.6}{Other Examples}{section.4}% 73
\BOOKMARK [2][-]{subsection.4.7}{Level 35}{section.4}% 74
\BOOKMARK [2][-]{subsection.4.8}{Level 69: The first Af that is not isomorphic to Af}{section.4}% 75
\BOOKMARK [2][-]{subsection.4.9}{Level 195: An Af not isomorphic to its dual, though there are solutions to the norm equation}{section.4}% 76