1
\providecommand{\bysame}{\leavevmode\hbox to3em{\hrulefill}\thinspace}
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\begin{thebibliography}{10}
3

4
\bibitem{agashe}
5
A.~Agash\'{e}, \emph{On invisible elements of the {T}ate-{S}hafarevich group},
6
  C. R. Acad. Sci. Paris S\'er. I Math. \textbf{328} (1999), no.~5, 369--374.
7

8
\bibitem{agashe:phd}
9
A.~Agashe, \emph{The {B}irch and {S}winnerton-{D}yer formula for modular
10
  abelian varieties of analytic rank~$0$}, U.\thinspace{}C. Berkeley Ph.D.
11
  thesis (2000).
12

13
\bibitem{agashe-stein:manin}
14
A.~Agashe and W.\thinspace{}A. Stein, \emph{On the generalized manin constant
15
  for quotients of \protect{$J_0(N)$}}, in preparation.
16

17
\bibitem{atkin-lehner}
18
A.\thinspace{}O.\thinspace{}L. Atkin and J.~Lehner, \emph{Hecke operators on
19
  \protect{$\Gamma \sb{0}(m)$}}, Math. Ann. \textbf{185} (1970), 134--160.
20

21
\bibitem{birch:atkin}
22
B.~Birch, \emph{Atkin and the {A}tlas {L}ab}, Proceedings of the conference in
23
  honor of A.\thinspace{}O.\thinspace{}L. Atkin held at the University of
24
  Illinois, Chicago, IL, September 1995, Amer. Math. Soc., Providence, RI,
25
  1998, pp.~13--20.
26

27
\bibitem{antwerpiv}
28
B.\thinspace{}J. Birch and W.~Kuyk (eds.), \emph{Modular functions of one
29
  variable. {I}{V}}, Springer-Verlag, Berlin, 1975, Lecture Notes in
30
  Mathematics, Vol. 476.
31

32
\bibitem{bloch-kato}
33
S.~Bloch and K.~Kato, \emph{\protect{${L}$}-functions and \protect{T}amagawa
34
  numbers of motives}, The Grothendieck Festschrift, Vol. \protect{I},
35
  Birkh\"auser Boston, Boston, MA, 1990, pp.~333--400.
36

37
\bibitem{neronmodels}
38
S.~Bosch, W.~L{\"u}tkebohmert, and M.~Raynaud, \emph{N\'eron models},
39
  Springer-Verlag, Berlin, 1990.
40

41
\bibitem{magma}
42
W.~Bosma, J.~Cannon, and C.~Playoust, \emph{The {M}agma algebra system {I}:
43
  {T}he user language}, J. Symb. Comp. \textbf{24} (1997), no.~3-4, 235--265,
44
  \\\protect{\sf http://www.maths.usyd.edu.au:8000/u/magma/}.
45

46
\bibitem{breuil-conrad-diamond-taylor}
47
C.~Breuil, B.~Conrad, F.~Diamond, and R.~Taylor, \emph{On the modularity of
48
  elliptic curves over \protect{$\Q$}, or {W}ild $3$-adic exercises},  (2000),
49
  \\\protect{\sf
50
  http://www.math.harvard.edu/HTML/Individuals/Richard\_Taylor.html}.
51

52
\bibitem{brumer:rank}
53
A.~Brumer, \emph{The rank of \protect{${J}\sb 0({N})$}}, Ast\'erisque (1995),
54
  no.~228, 3, 41--68, Columbia University Number Theory Seminar (New York,
55
  1992).
56

57
\bibitem{buzzard-stein:artin}
58
K.~Buzzard and W.\thinspace{}A. Stein, \emph{Modularity of some icosahedral
59
  {G}alois representations}, in preparation.
60

61
\bibitem{cohen-oesterle:dimensions}
62
H.~Cohen and J.~Oesterl{\'e}, \emph{Dimensions des espaces de formes
63
  modulaires},  (1977), 69--78. Lecture Notes in Math., Vol. 627.
64

65
\bibitem{coleman:monodromy}
66
R.~Coleman, \emph{The monodromy pairing}, Asian Math. Journal (1999).
67

68
\bibitem{cremona:gammaone}
69
J.\thinspace{}E. Cremona, \emph{Modular symbols for \protect{$\Gamma\sb
70
  1({N})$} and elliptic curves with everywhere good reduction}, Math. Proc.
71
  Cambridge Philos. Soc. \textbf{111} (1992), no.~2, 199--218.
72

73
\bibitem{cremona:algs}
74
\bysame, \emph{Algorithms for modular elliptic curves}, second ed., Cambridge
75
  University Press, Cambridge, 1997.
76

77
\bibitem{cremona:periods}
78
\bysame, \emph{Computing periods of cusp forms and modular elliptic curves},
79
  Experiment. Math. \textbf{6} (1997), no.~2, 97--107.
80

81
\bibitem{cremona-mazur}
82
J.\thinspace{}E. Cremona and B.~Mazur, \emph{Visualizing elements in the
83
  \protect{Shafarevich-Tate} group}, to appear in Experiment. Math.
84

85
\bibitem{darmon-bsd}
86
H.~Darmon, \emph{Wiles' theorem and the arithmetic of elliptic curves}, Modular
87
  forms and Fermat's last theorem (Boston, MA, 1995), Springer, New York, 1997,
88
  pp.~549--569.
89

90
\bibitem{darmon-merel}
91
H.~Darmon and L.~Merel, \emph{Winding quotients and some variants of {F}ermat's
92
  last theorem}, J. Reine Angew. Math. \textbf{490} (1997), 81--100.
93

94
\bibitem{diamond-im}
95
F.~Diamond and J.~Im, \emph{Modular forms and modular curves}, Seminar on
96
  {F}ermat's {L}ast {T}heorem, Providence, RI, 1995, pp.~39--133.
97

98
\bibitem{dummigan:cp}
99
N.~Dummigan, \emph{Period ratios of modular forms}, to appear in Math. Annalen.
100

101
\bibitem{edixhoven:eisen}
102
B.~Edixhoven, \emph{L'action de l'alg\`ebre de \protect{H}ecke sur les groupes
103
  de composantes des jacobiennes des courbes modulaires est
104
  ``\protect{E}isenstein''}, Ast\'erisque (1991), no.~196--197, 7--8, 159--170
105
  (1992), Courbes modulaires et courbes de Shimura (Orsay, 1987/1988).
106

107
\bibitem{empirical}
108
E.\thinspace{}V. Flynn, F.~\protect{Lepr\'{e}vost}, E.\thinspace{}F. Schaefer,
109
  W.\thinspace{}A. Stein, M.~Stoll, and J.\thinspace{}L. Wetherell,
110
  \emph{Empirical evidence for the \protect{B}irch and
111
  \protect{S}winnerton-\protect{D}yer conjectures for modular
112
  \protect{J}acobians of genus 2 curves}, Math. of Comp. (2000).
113

114
\bibitem{goldfeld:complexity}
115
D.~Goldfeld, \emph{On the computational complexity of modular symbols}, Math.
116
  Comp. \textbf{58} (1992), no.~198, 807--814.
117

118
\bibitem{ganz-lario:manin}
119
J.~Gonz\'{a}lez and J-C. Lario, \emph{$\mathbf{Q}$-curves and their {M}anin
120
  ideals}, preprint (2000).
121

122
\bibitem{gross-zagier}
123
B.~Gross and D.~Zagier, \emph{Heegner points and derivatives of
124
  \protect{${L}$}-series}, Invent. Math. \textbf{84} (1986), no.~2, 225--320.
125

126
\bibitem{gross:central}
127
B.\thinspace{}H. Gross, \emph{${L}$-functions at the central critical point},
128
  Motives (Seattle, WA, 1991), Amer. Math. Soc., Providence, RI, 1994,
129
  pp.~527--535.
130

131
\bibitem{hatada:rationality}
132
K.~Hatada, \emph{Multiplicity one theorem and modular symbols}, J. Math. Soc.
133
  Japan \textbf{33} (1981), no.~3, 445--470.
134

135
\bibitem{hijikata:trace}
136
H.~Hijikata, \emph{Explicit formula of the traces of \protect{H}ecke operators
137
  for \protect{$\Gamma_0(N)$}}, J. Math. Soc. Japan \textbf{26} (1974), no.~1,
138
  56--82.
139

140
\bibitem{katzmazur}
141
N.\thinspace{}M. Katz and B.~Mazur, \emph{Arithmetic moduli of elliptic
142
  curves}, Princeton University Press, Princeton, N.J., 1985.
143

144
\bibitem{kohel:hecke}
145
D.\thinspace{}R. Kohel, \emph{Hecke module structure of quaternions}, preprint
146
  (1998).
147

148
\bibitem{kolyvagin:mordellweil}
149
V.\thinspace{}A. Kolyvagin, \emph{On the {M}ordell-{W}eil group and the
150
  {S}hafarevich-{T}ate group of modular elliptic curves}, Proceedings of the
151
  International Congress of Mathematicians, Vol.\ I, II (Kyoto, 1990) (Tokyo),
152
  Math. Soc. Japan, 1991, pp.~429--436.
153

154
\bibitem{kolyvagin:structureofsha}
155
\bysame, \emph{On the structure of {S}hafarevich-{T}ate groups}, Algebraic
156
  geometry (Chicago, IL, 1989), Springer, Berlin, 1991, pp.~94--121.
157

158
\bibitem{kolyvagin-logachev:totallyreal}
159
V.\thinspace{}A. Kolyvagin and D.\thinspace{}Y. Logachev, \emph{Finiteness of
160
  \protect{$\Sha$} over totally real fields}, Math. USSR Izvestiya \textbf{39}
161
  (1992), no.~1, 829--853.
162

163
\bibitem{lang:algebra}
164
S.~Lang, \emph{Algebra}, third ed., Addison-Wesley Publishing Co., Reading,
165
  Mass., 1993.
166

167
\bibitem{winnie:newforms}
168
W-C. Li, \emph{Newforms and functional equations}, Math. Ann. \textbf{212}
169
  (1975), 285--315.
170

171
\bibitem{manin:parabolic}
172
J.\thinspace{}I. Manin, \emph{Parabolic points and zeta functions of modular
173
  curves}, Izv. Akad. Nauk SSSR Ser. Mat. \textbf{36} (1972), 19--66.
174

175
\bibitem{mazur:symboles}
176
B.~Mazur, \emph{Courbes elliptiques et symboles modulaires}, S\'eminaire
177
  Bourbaki, 24\`eme ann\'ee (1971/1972), Exp. No. 414, Springer, Berlin, 1973,
178
  pp.~277--294. Lecture Notes in Math., Vol. 317.
179

180
\bibitem{mazur:eisenstein}
181
\bysame, \emph{Modular curves and the \protect{Eisenstein} ideal}, Inst. Hautes
182
  \'Etudes Sci. Publ. Math. (1977), no.~47, 33--186 (1978).
183

184
\bibitem{mazur:rational}
185
\bysame, \emph{Rational isogenies of prime degree (with an appendix by {D}.
186
  {G}oldfeld)}, Invent. Math. \textbf{44} (1978), no.~2, 129--162.
187

188
\bibitem{mazur:arithmetic_values}
189
\bysame, \emph{On the arithmetic of special values of ${L}$\ functions},
190
  Invent. Math. \textbf{55} (1979), no.~3, 207--240.
191

192
\bibitem{mazur:visthree}
193
\bysame, \emph{Visualizing elements of order three in the {S}hafarevich-{T}ate
194
  group}, preprint (1999).
195

196
\bibitem{mazur-sd}
197
B.~Mazur and P.~Swinnerton-Dyer, \emph{Arithmetic of {W}eil curves}, Invent.
198
  Math. \textbf{25} (1974), 1--61.
199

200
\bibitem{merel:1585}
201
L.~Merel, \emph{Universal \protect{F}ourier expansions of modular forms}, On
202
  {A}rtin's conjecture for odd 2-dimensional representations (Berlin),
203
  Springer, 1994, pp.~59--94.
204

205
\bibitem{merel:weil}
206
\bysame, \emph{L'accouplement de {W}eil entre le sous-groupe de {S}himura et le
207
  sous-groupe cuspidal de ${J}\sb 0(p)$}, J. Reine Angew. Math. \textbf{477}
208
  (1996), 71--115.
209

210
\bibitem{mestre:graphs}
211
J.-F. Mestre, \emph{La m\'ethode des graphes. \protect{Exemples} et
212
  applications}, Proceedings of the international conference on class numbers
213
  and fundamental units of algebraic number fields (Katata) (1986), 217--242.
214

215
\bibitem{mestre-oesterle:crelle}
216
J.-F. Mestre and J.~Oesterl{\'e}, \emph{Courbes de {W}eil semi-stables de
217
  discriminant une puissance \protect{$m$}-i\`eme}, J. Reine Angew. Math.
218
  \textbf{400} (1989), 173--184.
219

220
\bibitem{milne:etale}
221
J.\thinspace{}S. Milne, \emph{\'{E}tale cohomology}, Princeton University
222
  Press, Princeton, N.J., 1980.
223

224
\bibitem{milne:abvars}
225
\bysame, \emph{Abelian varieties}, Arithmetic geometry (Storrs, Conn., 1984),
226
  Springer, New York, 1986, pp.~103--150.
227

228
\bibitem{milne:duality}
229
\bysame, \emph{Arithmetic duality theorems}, Academic Press Inc., Boston,
230
  Mass., 1986.
231

232
\bibitem{pizer:alg}
233
A.~Pizer, \emph{An algorithm for computing modular forms on
234
  \protect{$\Gamma\sb{0}({N})$}}, J. Algebra \textbf{64} (1980), no.~2,
235
  340--390.
236

237
\bibitem{ribet:modreps}
238
K.\thinspace{}A. Ribet, \emph{On modular representations of \protect{${\rm
239
  {G}al}(\overline{\bf{Q}}/{\bf {Q}})$} arising from modular forms}, Invent.
240
  Math. \textbf{100} (1990), no.~2, 431--476.
241

242
\bibitem{ribet:raising}
243
\bysame, \emph{Raising the levels of modular representations}, S\'eminaire de
244
  Th\'eorie des Nombres, Paris 1987--88, Birkh\"auser Boston, Boston, MA, 1990,
245
  pp.~259--271.
246

247
\bibitem{rubin:main-conjectures}
248
K.~Rubin, \emph{The ``main conjectures'' of {I}wasawa theory for imaginary
249
  quadratic fields}, Invent. Math. \textbf{103} (1991), no.~1, 25--68.
250

251
\bibitem{rubin:book}
252
\bysame, \emph{{E}uler {S}ystems}, Princeton University Press, Spring 2000,
253
  {A}nnals of {M}athematics {S}tudies {\bf 147}, \protect{\sf
254
  http://math.Stanford.EDU/\~{ }rubin/weyl.html}.
255

256
\bibitem{scholl:motivesinvent}
257
A.\thinspace{}J. Scholl, \emph{Motives for modular forms}, Invent. Math.
258
  \textbf{100} (1990), no.~2, 419--430.
259

260
\bibitem{scholl:kato}
261
\bysame, \emph{An introduction to {K}ato's {E}uler systems}, Galois
262
  Representations in Arithmetic Algebraic Geometry, Cambridge University Press,
263
  1998, pp.~379--460.
264

265
\bibitem{shafarevich:exp}
266
I.\thinspace{}R. Shafarevich, \emph{Exponents of elliptic curves}, Dokl. Akad.
267
  Nauk SSSR (N.S.) \textbf{114} (1957), 714--716.
268

269
\bibitem{shimura:surles}
270
G.~Shimura, \emph{Sur les \protect{int\'egrales} \protect{attach\'ees} aux
271
  formes automorphes}, J. Math. Soc. Japan \textbf{11} (1959), 291--311.
272

273
\bibitem{shimura:factors}
274
\bysame, \emph{On the factors of the jacobian variety of a modular function
275
  field}, J. Math. Soc. Japan \textbf{25} (1973), no.~3, 523--544.
276

277
\bibitem{shimura:intro}
278
\bysame, \emph{Introduction to the arithmetic theory of automorphic functions},
279
  Princeton University Press, Princeton, NJ, 1994, Reprint of the 1971
280
  original, Kan Memorial Lectures, 1.
281

282
\bibitem{sokurov:modsym}
283
V.~V. {\v{S}}okurov, \emph{Modular symbols of arbitrary weight}, Funkcional.
284
  Anal. i Prilo\v zen. \textbf{10} (1976), no.~1, 95--96.
285

286
\bibitem{stein:hecke}
287
W.\thinspace{}A. Stein, \emph{\protect{{\tt HECKE}: The} modular symbols
288
  calculator}, Software (available online) (1999).
289

290
\bibitem{stevens:thesis}
291
G.~Stevens, \emph{Arithmetic on modular curves}, Birkh\"auser Boston Inc.,
292
  Boston, Mass., 1982.
293

294
\bibitem{sturm:cong}
295
J.~Sturm, \emph{On the congruence of modular forms}, Number theory (New York,
296
  1984--1985), Springer, Berlin, 1987, pp.~275--280.
297

298
\bibitem{tate:bsd}
299
J.~Tate, \emph{On the conjectures of {B}irch and {S}winnerton-{D}yer and a
300
  geometric analog}, S\'eminaire Bourbaki, Vol.\ 9, Soc. Math. France, Paris,
301
  1995, pp.~Exp.\ No.\ 306, 415--440.
302

303
\bibitem{cime-1997}
304
C.~Viola, \emph{{Arithmetic theory of elliptic curves. Lectures given at the
305
  3rd session of the {C}entro {I}nternazionale {M}atematico {E}stivo
306
  \protect{(CIME)}.}}, Springer-Verlag, Berlin, 1997 (English).
307

308
\bibitem{zagier:parametrizations}
309
D.~Zagier, \emph{Modular parametrizations of elliptic curves}, Canad. Math.
310
  Bull. \textbf{28} (1985), no.~3, 372--384.
311

312
\end{thebibliography}
313