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\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}
}
\providecommand{\href}[2]{#2}
\begin{thebibliography}{BCDT01}

\bibitem[AS]{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[AS02]{agashe-stein:visibility}
\bysame, \emph{Visibility of {S}hafarevich-{T}ate groups of abelian varieties},
  J. Number Theory \textbf{97} (2002), no.~1, 171--185. \MR{2003h:11070}

\bibitem[BCDT01]{breuil-conrad-diamond-taylor}
C.~Breuil, B.~Conrad, F.~Diamond, and R.~Taylor, \emph{On the modularity of
  elliptic curves over {$\bold Q$}: wild 3-adic exercises}, J. Amer. Math. Soc.
  \textbf{14} (2001), no.~4, 843--939 (electronic). \MR{2002d:11058}

\bibitem[BCP97]{magma}
W.~Bosma, J.~Cannon, and C.~Playoust, \emph{The {M}agma algebra system. {I}.
  {T}he user language}, J. Symbolic Comput. \textbf{24} (1997), no.~3-4,
  235--265, Computational algebra and number theory (London, 1993). \MR{1 484
  478}

\bibitem[Bir71]{birch:bsd}
B.\thinspace{}J. Birch, \emph{Elliptic curves over \protect{${\mathbf{Q}}$:
  {A}} progress report}, 1969 Number Theory Institute (Proc. Sympos. Pure
  Math., Vol. XX, State Univ. New York, Stony Brook, N.Y., 1969), Amer. Math.
  Soc., Providence, R.I., 1971, pp.~396--400.

\bibitem[CES03]{conrad-edixhoven-stein:j1p}
B.~Conrad, S.~Edixhoven, and W.\thinspace{}A. Stein, \emph{${J}_1(p)$ {H}as
  {C}onnected {F}ibers}, Documenta Mathematica \textbf{8} (2003), 331--408.

\bibitem[Cre]{cremona:onlinetables}
J.\thinspace{}E. Cremona, \emph{Elliptic curves of conductor \protect{$\leq
  17000$},\hfill\\ {\tt http://www.maths.nott.ac.uk/personal/jec/ftp/data/}}.

\bibitem[CS01]{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[DWS03]{dummigan-stein-watkins:motives}
N.~Dummigan, M.~Watkins, and W.\thinspace{}A. Stein, \emph{{Constructing
  Elements in Shafarevich-Tate Groups of Modular Motives}}, Number theory and
  algebraic geometry, ed. by Miles Reid and Alexei Skorobogatov \textbf{303}
  (2003), 91--118.

\bibitem[Eme01]{emerton:optimal}
M.~Emerton, \emph{Optimal {Q}uotients of {M}odular {J}acobians}, preprint
  (2001).

\bibitem[FpS{\etalchar{+}}01]{empirical}
E.\thinspace{}V. Flynn, F.~\protect{Lepr\'{e}vost}, E.\thinspace{}F. Schaefer,
  W.\thinspace{}A. Stein, M.~Stoll, and J.\thinspace{}L. Wetherell,
  \emph{Empirical evidence for the {B}irch and {S}winnerton-{D}yer conjectures
  for modular {J}acobians of genus 2 curves}, Math. Comp. \textbf{70} (2001),
  no.~236, 1675--1697 (electronic). \MR{1 836 926}

\bibitem[Kat]{kato:secret}
K.~Kato, \emph{$p$-adic {H}odge theory and values of zeta functions of modular
  forms}, Preprint, 244 pages.

\bibitem[KL81]{kubert-lang}
D.\thinspace{}S. Kubert and S.~Lang, \emph{Modular units}, Grundlehren der
  Mathematischen Wissenschaften [Fundamental Principles of Mathematical
  Science], vol. 244, Springer-Verlag, New York, 1981. \MR{84h:12009}

\bibitem[Lan91]{lang:nt3}
S.~Lang, \emph{Number theory. {I}{I}{I}}, Springer-Verlag, Berlin, 1991,
  Diophantine geometry. \MR{93a:11048}

\bibitem[Maz77]{mazur:eisenstein}
B.~Mazur, \emph{Modular curves and the \protect{Eisenstein} ideal}, Inst.
  Hautes \'Etudes Sci. Publ. Math. (1977), no.~47, 33--186 (1978).

\bibitem[Mer94]{merel:1585}
L.~Merel, \emph{Universal \protect{F}ourier expansions of modular forms}, On
  {A}rtin's conjecture for odd 2-dimensional representations, Springer, 1994,
  pp.~59--94.

\bibitem[Rib80]{ribet:twistsendoalg}
K.\thinspace{}A. Ribet, \emph{Twists of modular forms and endomorphisms of
  abelian varieties}, Math. Ann. \textbf{253} (1980), no.~1, 43--62.
  \MR{82e:10043}

\bibitem[Rib90]{ribet:raising}
\bysame, \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[Roh84]{rohrlich:cyclo}
D.\thinspace{}E. Rohrlich, \emph{On {$L$}-functions of elliptic curves and
  cyclotomic towers}, Invent. Math. \textbf{75} (1984), no.~3, 409--423.
  \MR{86g:11038b}

\bibitem[Rub98]{rubin:kato}
K.~Rubin, \emph{Euler systems and modular elliptic curves}, Galois
  representations in arithmetic algebraic geometry (Durham, 1996), Cambridge
  Univ. Press, Cambridge, 1998, pp.~351--367. \MR{2001a:11106}

\bibitem[Shi73]{shimura:factors}
G.~Shimura, \emph{On the factors of the jacobian variety of a modular function
  field}, J. Math. Soc. Japan \textbf{25} (1973), no.~3, 523--544.

\bibitem[Ste03a]{mfd}
W.\thinspace{}A. Stein, \emph{The {M}odular {F}orms {D}atabase}, \newline{\tt
  http://modular.fas.harvard.edu/Tables} (2003).

\bibitem[Ste03b]{stein:bsdmagma}
\bysame, \emph{Studying the {B}irch and {S}winnerton-{D}yer {C}onjecture for
  {M}odular {A}belian {V}arieties {U}sing {MAGMA}}, To appear in J.~Cannon,
  ed., {\em Computational Experiments in Algebra and Geometry}, Springer-Verlag
  (2003).

\bibitem[Ste04]{stein:nonsquaresha}
\bysame, \emph{Shafarevich-tate groups of nonsquare order}, Proceedings of MCAV
  2002, Progress of Mathematics (2004), 277--289.

\bibitem[Tat66]{tate:bsd}
J.~Tate, \emph{On the conjectures of {B}irch and {S}winnerton-{D}yer and a
  geometric analog}, S\'eminaire Bourbaki, Vol.\ 9, Soc. Math. France, Paris,
  1965/66, pp.~Exp.\ No.\ 306, 415--440.

\end{thebibliography}
