\relax 
\@input{abstract.aux}
\@writefile{toc}{\contentsline {chapter}{List of Figures}{v}}
\citation{cremona-mazur}
\@writefile{toc}{\contentsline {chapter}{List of Tables}{vi}}
\@input{symbols.aux}
\@input{preface.aux}
\@input{bsd.aux}
\@input{modsyms.aux}
\@input{algorithms.aux}
\@input{compgroup.aux}
\bibstyle{amsplain}
\bibdata{biblio}
\bibcite{agashe}{1}
\bibcite{agashe:phd}{2}
\bibcite{agashe-stein:manin}{3}
\bibcite{atkin-lehner}{4}
\bibcite{birch:atkin}{5}
\bibcite{antwerpiv}{6}
\bibcite{bloch-kato}{7}
\bibcite{neronmodels}{8}
\bibcite{magma}{9}
\bibcite{breuil-conrad-diamond-taylor}{10}
\bibcite{brumer:rank}{11}
\bibcite{buzzard-stein:artin}{12}
\bibcite{cohen-oesterle:dimensions}{13}
\@writefile{toc}{\contentsline {chapter}{Bibliography}{88}}
\bibcite{coleman:monodromy}{14}
\bibcite{cremona:gammaone}{15}
\bibcite{cremona:algs}{16}
\bibcite{cremona:periods}{17}
\bibcite{cremona-mazur}{18}
\bibcite{darmon-bsd}{19}
\bibcite{darmon-merel}{20}
\bibcite{diamond-im}{21}
\bibcite{dummigan:cp}{22}
\bibcite{edixhoven:eisen}{23}
\bibcite{empirical}{24}
\bibcite{goldfeld:complexity}{25}
\bibcite{ganz-lario:manin}{26}
\bibcite{gross-zagier}{27}
\bibcite{gross:central}{28}
\bibcite{hatada:rationality}{29}
\bibcite{hijikata:trace}{30}
\bibcite{katzmazur}{31}
\bibcite{kohel:hecke}{32}
\bibcite{kolyvagin:mordellweil}{33}
\bibcite{kolyvagin:structureofsha}{34}
\bibcite{kolyvagin-logachev:totallyreal}{35}
\bibcite{lang:algebra}{36}
\bibcite{winnie:newforms}{37}
\bibcite{manin:parabolic}{38}
\bibcite{mazur:symboles}{39}
\bibcite{mazur:eisenstein}{40}
\bibcite{mazur:rational}{41}
\bibcite{mazur:arithmetic_values}{42}
\bibcite{mazur:visthree}{43}
\bibcite{mazur-sd}{44}
\bibcite{merel:1585}{45}
\bibcite{merel:weil}{46}
\bibcite{mestre:graphs}{47}
\bibcite{mestre-oesterle:crelle}{48}
\bibcite{milne:etale}{49}
\bibcite{milne:abvars}{50}
\bibcite{milne:duality}{51}
\bibcite{pizer:alg}{52}
\bibcite{ribet:modreps}{53}
\bibcite{ribet:raising}{54}
\bibcite{rubin:main-conjectures}{55}
\bibcite{rubin:book}{56}
\bibcite{scholl:motivesinvent}{57}
\bibcite{scholl:kato}{58}
\bibcite{shafarevich:exp}{59}
\bibcite{shimura:surles}{60}
\bibcite{shimura:factors}{61}
\bibcite{shimura:intro}{62}
\bibcite{sokurov:modsym}{63}
\bibcite{stein:hecke}{64}
\bibcite{stevens:thesis}{65}
\bibcite{sturm:cong}{66}
\bibcite{tate:bsd}{67}
\bibcite{cime-1997}{68}
\bibcite{zagier:parametrizations}{69}
