\relax 
\providecommand\HyperFirstAtBeginDocument{\AtBeginDocument}
\HyperFirstAtBeginDocument{\ifx\hyper@anchor\@undefined
\global\let\oldcontentsline\contentsline
\gdef\contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}}
\global\let\oldnewlabel\newlabel
\gdef\newlabel#1#2{\newlabelxx{#1}#2}
\gdef\newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}}
\AtEndDocument{\ifx\hyper@anchor\@undefined
\let\contentsline\oldcontentsline
\let\newlabel\oldnewlabel
\fi}
\fi}
\global\let\hyper@last\relax 
\gdef\HyperFirstAtBeginDocument#1{#1}
\providecommand\HyField@AuxAddToFields[1]{}
\citation{ribet-stein:pcmi}
\citation{eisenstein}
\citation{eisenstein}
\citation{eisenstein}
\citation{eisenstein}
\@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{1}{section.1}}
\newlabel{theorem:rank}{{1.1}{1}{Mazur\relax }{theorem.1.1}{}}
\citation{agashe-stein:bsd}
\citation{Ribet}
\citation{Ribet}
\citation{Ribet}
\citation{ribet:congrel}
\@writefile{toc}{\contentsline {section}{\numberline {2}The Abelian Variety $A$}{3}{section.2}}
\newlabel{sec:abvarA}{{2}{3}{The Abelian Variety $A$\relax }{section.2}{}}
\newlabel{theorem:computations}{{2.1}{3}{\relax }{theorem.2.1}{}}
\newlabel{thm_p1}{{2.1}{3}{\relax }{theorem.2.1}{}}
\newlabel{thm_p2}{{2.1}{3}{\relax }{theorem.2.1}{}}
\newlabel{thm_p3}{{2.1}{3}{\relax }{theorem.2.1}{}}
\citation{eisenstein}
\citation{lario-schoof}
\citation{lario-schoof}
\newlabel{thm_p4}{{2.1}{4}{\relax }{theorem.2.1}{}}
\newlabel{lem:witt}{{2.3}{4}{\relax }{theorem.2.3}{}}
\newlabel{lemma:equal}{{2.5}{4}{\relax }{theorem.2.5}{}}
\citation{eisenstein}
\citation{OT}
\citation{eisenstein}
\citation{eisenstein}
\newlabel{lemma:maximal}{{2.6}{5}{\relax }{theorem.2.6}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.1}Determining the Jordan--H\"{o}lder factors of $A[\mathfrak  {m}]$}{5}{subsection.2.1}}
\citation{eisenstein}
\newlabel{lemma:above}{{2.9}{6}{\relax }{Item.8}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.2}Determining $A[\mathfrak  {m}]$}{6}{subsection.2.2}}
\newlabel{lemma:extra}{{2.10}{6}{\relax }{theorem.2.10}{}}
\newlabel{lemma:contra}{{2.11}{7}{\relax }{theorem.2.11}{}}
\newlabel{lemma:sofarupyouforgotit}{{2.13}{8}{\relax }{theorem.2.13}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.3}The torsion subgroup of $A$ and $A^{\vee }$}{9}{subsection.2.3}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.4}Conjectural Computations with the BSD conjecture}{10}{subsection.2.4}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.5}Remarks on the Structure of the Tate Module}{10}{subsection.2.5}}
\citation{eisenstein}
\@writefile{toc}{\contentsline {section}{\numberline {3}The Descent}{11}{section.3}}
\newlabel{lemma:prep}{{3.1}{11}{\relax }{theorem.3.1}{}}
\citation{eisenstein}
\citation{eisenstein}
\citation{eisenstein}
\citation{eisenstein}
\citation{iwasawa}
\citation{sage}
\@writefile{toc}{\contentsline {section}{\numberline {4}Algorithmic Computations}{13}{section.4}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.1}The quotient by the Eisenstein ideal}{14}{subsection.4.1}}
\newlabel{sec:quo_eis}{{4.1}{14}{The quotient by the Eisenstein ideal\relax }{subsection.4.1}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.2}The 15-dimensional abelian variety $A$}{15}{subsection.4.2}}
\newlabel{sec:A15}{{4.2}{15}{The 15-dimensional abelian variety $A$\relax }{subsection.4.2}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.3}The Index of $\mathcal  {O}_\mathfrak  {m}$ in its integral closure}{15}{subsection.4.3}}
\newlabel{sec:indexOm}{{4.3}{15}{The Index of $\O _\m $ in its integral closure\relax }{subsection.4.3}{}}
\citation{kohel-stein:ants4}
\bibcite{agashe-stein:bsd}{AS05}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.4}The modular degree of $A$}{17}{subsection.4.4}}
\newlabel{sec:moddeg}{{4.4}{17}{The modular degree of $A$\relax }{subsection.4.4}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.5}The kernels of ideals acting on $A$}{17}{subsection.4.5}}
\newlabel{sec:kernels}{{4.5}{17}{The kernels of ideals acting on $A$\relax }{subsection.4.5}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.6}Simultaneous pathologies}{17}{subsection.4.6}}
\newlabel{sec:pathology}{{4.6}{17}{Simultaneous pathologies\relax }{subsection.4.6}{}}
\bibcite{CE}{1}
\bibcite{lario-schoof}{2}
\bibcite{eisenstein}{3}
\bibcite{iwasawa}{4}
\bibcite{kohel-stein:ants4}{KS00}
\bibcite{OT}{5}
\bibcite{Raynaud}{6}
\bibcite{Ribet}{7}
\bibcite{ribet:congrel}{8}
\bibcite{ribet-stein:pcmi}{9}
\bibcite{sage}{S{{+}}11}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.7}Computing the minimal degree of an isogeny to the dual}{18}{subsection.4.7}}
\newlabel{sec:minisog}{{4.7}{18}{Computing the minimal degree of an isogeny to the dual\relax }{subsection.4.7}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.8}Table of minimal isogeny degrees}{18}{subsection.4.8}}
\newlabel{sec:minisog_table}{{4.8}{18}{Table of minimal isogeny degrees\relax }{subsection.4.8}{}}
