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\begin{thebibliography}{BCDT01}
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\bibitem[AS]{agashe-stein:bsd}
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A.~Agashe and W.\thinspace{}A. Stein, \emph{Visible {E}vidence for the {B}irch
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and {S}winnerton-{D}yer {C}onjecture for {M}odular {A}belian {V}arieties of
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{A}nalytic {R}ank~$0$}, To appear in Math. of Computation.
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\bibitem[AS02]{agashe-stein:visibility}
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\bysame, \emph{Visibility of {S}hafarevich-{T}ate groups of abelian varieties},
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J. Number Theory \textbf{97} (2002), no.~1, 171--185. \MR{2003h:11070}
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\bibitem[BCDT01]{breuil-conrad-diamond-taylor}
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C.~Breuil, B.~Conrad, F.~Diamond, and R.~Taylor, \emph{On the modularity of
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elliptic curves over {$\bold Q$}: wild 3-adic exercises}, J. Amer. Math. Soc.
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\textbf{14} (2001), no.~4, 843--939 (electronic). \MR{2002d:11058}
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\bibitem[BCP97]{magma}
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W.~Bosma, J.~Cannon, and C.~Playoust, \emph{The {M}agma algebra system. {I}.
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{T}he user language}, J. Symbolic Comput. \textbf{24} (1997), no.~3-4,
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235--265, Computational algebra and number theory (London, 1993). \MR{1 484
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478}
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\bibitem[Bir71]{birch:bsd}
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B.\thinspace{}J. Birch, \emph{Elliptic curves over \protect{${\mathbf{Q}}$:
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{A}} progress report}, 1969 Number Theory Institute (Proc. Sympos. Pure
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Math., Vol. XX, State Univ. New York, Stony Brook, N.Y., 1969), Amer. Math.
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Soc., Providence, R.I., 1971, pp.~396--400.
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\bibitem[CES03]{conrad-edixhoven-stein:j1p}
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B.~Conrad, S.~Edixhoven, and W.\thinspace{}A. Stein, \emph{${J}_1(p)$ {H}as
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{C}onnected {F}ibers}, Documenta Mathematica \textbf{8} (2003), 331--408.
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\bibitem[Cre]{cremona:onlinetables}
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J.\thinspace{}E. Cremona, \emph{Elliptic curves of conductor \protect{$\leq
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17000$},\hfill\\ {\tt http://www.maths.nott.ac.uk/personal/jec/ftp/data/}}.
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\bibitem[CS01]{conrad-stein:compgroup}
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Brian Conrad and William~A. Stein, \emph{Component groups of purely toric
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quotients}, Math. Res. Lett. \textbf{8} (2001), no.~5-6, 745--766.
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\MR{2003f:11087}
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\bibitem[DWS03]{dummigan-stein-watkins:motives}
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N.~Dummigan, M.~Watkins, and W.\thinspace{}A. Stein, \emph{{Constructing
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Elements in Shafarevich-Tate Groups of Modular Motives}}, Number theory and
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algebraic geometry, ed. by Miles Reid and Alexei Skorobogatov \textbf{303}
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(2003), 91--118.
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\bibitem[Eme01]{emerton:optimal}
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M.~Emerton, \emph{Optimal {Q}uotients of {M}odular {J}acobians}, preprint
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(2001).
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\bibitem[FpS{\etalchar{+}}01]{empirical}
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E.\thinspace{}V. Flynn, F.~\protect{Lepr\'{e}vost}, E.\thinspace{}F. Schaefer,
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W.\thinspace{}A. Stein, M.~Stoll, and J.\thinspace{}L. Wetherell,
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\emph{Empirical evidence for the {B}irch and {S}winnerton-{D}yer conjectures
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for modular {J}acobians of genus 2 curves}, Math. Comp. \textbf{70} (2001),
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no.~236, 1675--1697 (electronic). \MR{1 836 926}
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\bibitem[Kat]{kato:secret}
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K.~Kato, \emph{$p$-adic {H}odge theory and values of zeta functions of modular
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forms}, Preprint, 244 pages.
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\bibitem[KL81]{kubert-lang}
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D.\thinspace{}S. Kubert and S.~Lang, \emph{Modular units}, Grundlehren der
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Mathematischen Wissenschaften [Fundamental Principles of Mathematical
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Science], vol. 244, Springer-Verlag, New York, 1981. \MR{84h:12009}
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\bibitem[Lan91]{lang:nt3}
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S.~Lang, \emph{Number theory. {I}{I}{I}}, Springer-Verlag, Berlin, 1991,
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Diophantine geometry. \MR{93a:11048}
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\bibitem[Maz77]{mazur:eisenstein}
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B.~Mazur, \emph{Modular curves and the \protect{Eisenstein} ideal}, Inst.
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Hautes \'Etudes Sci. Publ. Math. (1977), no.~47, 33--186 (1978).
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\bibitem[Mer94]{merel:1585}
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L.~Merel, \emph{Universal \protect{F}ourier expansions of modular forms}, On
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{A}rtin's conjecture for odd 2-dimensional representations, Springer, 1994,
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pp.~59--94.
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\bibitem[Rib80]{ribet:twistsendoalg}
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K.\thinspace{}A. Ribet, \emph{Twists of modular forms and endomorphisms of
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abelian varieties}, Math. Ann. \textbf{253} (1980), no.~1, 43--62.
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\MR{82e:10043}
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\bibitem[Rib90]{ribet:raising}
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\bysame, \emph{Raising the levels of modular representations}, S\'eminaire de
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Th\'eorie des Nombres, Paris 1987--88, Birkh\"auser Boston, Boston, MA, 1990,
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pp.~259--271.
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\bibitem[Roh84]{rohrlich:cyclo}
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D.\thinspace{}E. Rohrlich, \emph{On {$L$}-functions of elliptic curves and
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cyclotomic towers}, Invent. Math. \textbf{75} (1984), no.~3, 409--423.
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\MR{86g:11038b}
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\bibitem[Rub98]{rubin:kato}
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K.~Rubin, \emph{Euler systems and modular elliptic curves}, Galois
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representations in arithmetic algebraic geometry (Durham, 1996), Cambridge
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Univ. Press, Cambridge, 1998, pp.~351--367. \MR{2001a:11106}
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\bibitem[Shi73]{shimura:factors}
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G.~Shimura, \emph{On the factors of the jacobian variety of a modular function
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field}, J. Math. Soc. Japan \textbf{25} (1973), no.~3, 523--544.
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\bibitem[Ste03a]{mfd}
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W.\thinspace{}A. Stein, \emph{The {M}odular {F}orms {D}atabase}, \newline{\tt
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http://modular.fas.harvard.edu/Tables} (2003).
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\bibitem[Ste03b]{stein:bsdmagma}
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\bysame, \emph{Studying the {B}irch and {S}winnerton-{D}yer {C}onjecture for
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{M}odular {A}belian {V}arieties {U}sing {MAGMA}}, To appear in J.~Cannon,
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ed., {\em Computational Experiments in Algebra and Geometry}, Springer-Verlag
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(2003).
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\bibitem[Ste04]{stein:nonsquaresha}
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\bysame, \emph{Shafarevich-tate groups of nonsquare order}, Proceedings of MCAV
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2002, Progress of Mathematics (2004), 277--289.
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\bibitem[Tat66]{tate:bsd}
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J.~Tate, \emph{On the conjectures of {B}irch and {S}winnerton-{D}yer and a
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geometric analog}, S\'eminaire Bourbaki, Vol.\ 9, Soc. Math. France, Paris,
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1965/66, pp.~Exp.\ No.\ 306, 415--440.
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\end{thebibliography}
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