\relax 
\bibstyle{amsalpha}
\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{kolyvagin:structure_of_selmer}
\citation{kolyvagin:structure_of_selmer}
\citation{gross-zagier}
\citation{stein:kolyconj2}
\citation{cremona-mazur}
\citation{agashe-stein:visibility}
\citation{agashe-stein:bsd}
\citation{jetchev-stein:higher}
\citation{stein:vismw}
\citation{jetchev-lauter-stein}
\citation{stein:kolyconj2}
\@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{1}{section.1}}
\newlabel{sec:intro}{{1}{1}{Introduction\relax }{section.1}{}}
\newlabel{conj:koly}{{1.1}{1}{Kolyvagin\relax }{theorem.1.1}{}}
\@writefile{toc}{\contentsline {section}{\numberline {2}Theorems}{2}{section.2}}
\newlabel{sec:main}{{2}{2}{Theorems\relax }{section.2}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.1}Preliminaries}{2}{subsection.2.1}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.2}Elliptic Curves of the Same Conductor}{3}{subsection.2.2}}
\newlabel{thm:main}{{2.2}{3}{\relax }{theorem.2.2}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.3}Elliptic Curves of Different Conductors}{3}{subsection.2.3}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.4}Abelian Varieties}{3}{subsection.2.4}}
\@writefile{toc}{\contentsline {section}{\numberline {3}Algorithms}{3}{section.3}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.1}$p$-adic $L$-series}{3}{subsection.3.1}}
\@writefile{toc}{\contentsline {section}{\numberline {4}Tables}{3}{section.4}}
\newlabel{sec:example}{{4}{3}{Tables\relax }{section.4}{}}
\bibdata{biblio}
\bibcite{agashe-stein:visibility}{AS02}
\bibcite{agashe-stein:bsd}{AS05}
\bibcite{cremona-mazur}{CM00}
\bibcite{gross-zagier}{GZ86}
\bibcite{jetchev-lauter-stein}{JLS09}
\bibcite{jetchev-stein:higher}{JS07}
\bibcite{kolyvagin:structure_of_selmer}{Kol91}
\bibcite{stein:vismw}{Ste07}
\bibcite{stein:kolyconj2}{Ste11}
