\providecommand{\bysame}{\leavevmode\hbox to3em{\hrulefill}\thinspace}
\providecommand{\MR}{\relax\ifhmode\unskip\space\fi MR }
% \MRhref is called by the amsart/book/proc definition of \MR.
\providecommand{\MRhref}[2]{%
  \href{http://www.ams.org/mathscinet-getitem?mr=#1}{#2}
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\providecommand{\href}[2]{#2}
\begin{thebibliography}{10}

\bibitem{agashe-stein:bsd}
A.~Agashe and W.\thinspace{}A. Stein, \emph{Visible {E}vidence for the {B}irch
  and {S}winnerton-{D}yer {C}onjecture for {M}odular {A}belian {V}arieties of
  {A}nalytic {R}ank~$0$}, To appear in Math. of Computation.

\bibitem{agashe-stein:manin}
\bysame, \emph{The manin constant, congruence primes, and the modular degree},
  Preprint,\hfill\\ {\tt http://modular.fas.harvard.edu/papers/manin-agashe/}
  (2004).

\bibitem{neronmodels}
S.~Bosch, W.~L{\"u}tkebohmert, and M.~Raynaud, \emph{N\'eron models},
  Springer-Verlag, Berlin, 1990.

\bibitem{cassels:ellcurves}
J.\thinspace{}W.\thinspace{}S. Cassels, \emph{Lectures on elliptic curves},
  Cambridge University Press, Cambridge, 1991.

\bibitem{cassels-frohlich}
J.\thinspace{}W.\thinspace{}S. Cassels and A.~\protect{Fr{\"o}hlich} (eds.),
  \emph{Algebraic number theory}, London, Academic Press Inc. [Harcourt Brace
  Jovanovich Publishers], 1986, Reprint of the 1967 original.

\bibitem{conrad-stein:compgroup}
Brian Conrad and William~A. Stein, \emph{Component groups of purely toric
  quotients}, Math. Res. Lett. \textbf{8} (2001), no.~5-6, 745--766.
  \MR{2003f:11087}

\bibitem{cremona-mazur}
J.\thinspace{}E. Cremona and B.~Mazur, \emph{Visualizing elements in the
  {S}hafarevich-{T}ate group}, Experiment. Math. \textbf{9} (2000), no.~1,
  13--28. \MR{1 758 797}

\bibitem{ega4_2}
A.~Grothendieck, \emph{\'{E}l\'ements de g\'eom\'etrie alg\'ebrique. {I}{V}.
  \'{E}tude locale des sch\'emas et des morphismes de sch\'emas. {I}{I}}, Inst.
  Hautes \'Etudes Sci. Publ. Math. (1965), no.~24, 231. \MR{33 \#7330}

\bibitem{ega4_3}
\bysame, \emph{\'{E}l\'ements de g\'eom\'etrie alg\'ebrique. {I}{V}. \'{E}tude
  locale des sch\'emas et des morphismes de sch\'emas. {I}{I}{I}}, Inst. Hautes
  \'Etudes Sci. Publ. Math. (1966), no.~28, 255. \MR{36 \#178}

\bibitem{ega4_4}
\bysame, \emph{\'{E}l\'ements de g\'eom\'etrie alg\'ebrique. {I}{V}. \'{E}tude
  locale des sch\'emas et des morphismes de sch\'emas {I}{V}}, Inst. Hautes
  \'Etudes Sci. Publ. Math. (1967), no.~32, 361. \MR{39 \#220}

\bibitem{hartshorne}
R.~Hartshorne, \emph{Algebraic {G}eometry}, Springer-Verlag, New York, 1977,
  Graduate Texts in Mathematics, No. 52.

\bibitem{katz:torsion}
N.\thinspace{}M. Katz, \emph{Galois properties of torsion points on abelian
  varieties}, Invent. Math. \textbf{62} (1981), no.~3, 481--502. \MR{82d:14025}

\bibitem{kohel-stein:ants4}
D.\thinspace{}R. Kohel and W.\thinspace{}A. Stein, \emph{Component {G}roups of
  {Q}uotients of \protect{$J_0(N)$}}, Proceedings of the 4th International
  Symposium (ANTS-IV), Leiden, Netherlands, July 2--7, 2000 (Berlin), Springer,
  2000.

\bibitem{lang:ant}
S.~Lang, \emph{Algebraic number theory}, second ed., Springer-Verlag, New York,
  1994.

\bibitem{mazur:rational}
B.~Mazur, \emph{Rational isogenies of prime degree (with an appendix by {D}.
  {G}oldfeld)}, Invent. Math. \textbf{44} (1978), no.~2, 129--162.

\bibitem{milne:abvars}
J.\thinspace{}S. Milne, \emph{Abelian varieties}, Arithmetic geometry (Storrs,
  Conn., 1984), Springer, New York, 1986, pp.~103--150.

\bibitem{milne:duality}
\bysame, \emph{Arithmetic duality theorems}, Academic Press Inc., Boston,
  Mass., 1986.

\bibitem{milne:jacs}
\bysame, \emph{Jacobian varieties}, Arithmetic geometry (Storrs, Conn., 1984),
  Springer, New York, 1986, pp.~167--212.

\bibitem{mumford:abvars}
D.~Mumford, \emph{Abelian varieties}, Published for the Tata Institute of
  Fundamental Research, Bombay, 1970, Tata Institute of Fundamental Research
  Studies in Mathematics, No. 5.

\bibitem{mumford:jacs}
\bysame, \emph{Curves and their jacobians}, Ann Arbor, The University of
  Michigan Press, 1975.

\bibitem{ribet:raising}
K.\thinspace{}A. Ribet, \emph{Raising the levels of modular representations},
  S\'eminaire de Th\'eorie des Nombres, Paris 1987--88, Birkh\"auser Boston,
  Boston, MA, 1990, pp.~259--271.

\bibitem{shimura:intro}
G.~Shimura, \emph{Introduction to the arithmetic theory of automorphic
  functions}, Princeton University Press, Princeton, NJ, 1994, Reprint of the
  1971 original, Kan Memorial Lectures, 1.

\bibitem{silverman:aec}
J.\thinspace{}H. Silverman, \emph{The arithmetic of elliptic curves},
  Springer-Verlag, New York, 1992, Corrected reprint of the 1986 original.

\bibitem{silverman:aec2}
\bysame, \emph{Advanced topics in the arithmetic of elliptic curves},
  Springer-Verlag, New York, 1994.

\bibitem{stein:phd}
W.\thinspace{}A. Stein, \emph{Explicit approaches to modular abelian
  varieties}, Ph.D. thesis, University of California, Berkeley (2000).

\bibitem{stevens:thesis}
G.~Stevens, \emph{Arithmetic on modular curves}, Birkh\"auser Boston Inc.,
  Boston, Mass., 1982. \MR{87b:11050}

\bibitem{tate:antwerpiv}
J.~Tate, \emph{Algorithm for determining the type of a singular fiber in an
  elliptic pencil}, Modular functions of one variable, IV (Proc. Internat.
  Summer School, Univ. Antwerp, Antwerp, 1972), Springer, Berlin, 1975,
  pp.~33--52. Lecture Notes in Math., Vol. 476. \MR{52 \#13850}

\end{thebibliography}
