\relax \@writefile{toc}{\contentsline {section}{\numberline {1}Modular Abelian Varieties}{1}} \@writefile{toc}{\contentsline {section}{\numberline {2}The Birch and Swinnerton-Dyer Conjecture}{2}} \@writefile{toc}{\contentsline {subsection}{\numberline {2.1}Conjecture}{2}} \@writefile{toc}{\contentsline {subsection}{\numberline {2.2}Evidence}{3}} \@writefile{toc}{\contentsline {section}{\numberline {3}Visibility of Shafarevich-Tate Groups}{3}} \@writefile{toc}{\contentsline {subsection}{\numberline {3.1}Definitions}{3}} \newlabel{defn:sha}{{3.1}{3}} \@writefile{toc}{\contentsline {subsection}{\numberline {3.2}Theorems}{4}} \newlabel{vis:const}{{3.4}{4}} \@writefile{toc}{\contentsline {subsection}{\numberline {3.3}Example}{5}} \@writefile{toc}{\contentsline {section}{\numberline {4}Visibility in Modular Jacobians}{5}} \@writefile{toc}{\contentsline {subsection}{\numberline {4.1}Data and Experiments}{5}} \@writefile{toc}{\contentsline {section}{\numberline {5}Visibility at Higher Level}{6}} \@writefile{toc}{\contentsline {subsection}{\numberline {5.1}Ribet Level Raising}{6}} \@writefile{toc}{\contentsline {subsection}{\numberline {5.2}Evidence for Conjecture}{6}} \@writefile{toc}{\contentsline {section}{\numberline {6}Some Tables}{6}}