- 
 - Aga99b
 - 
A.Agashe, On invisible elements of the Tate-Shafarevich
  group, C. R. Acad. Sci. Paris Sér. I Math. 328 (1999), no. 5,
  369-374.
 - AS02
 - 
A.Agashe and W.A. Stein, Visibility of Shafarevich-Tate
  groups of abelian varieties, J. Number Theory 97 (2002), no. 1,
  171-185.
 - AS05
 - 
A. Agashe and W. Stein, Visible evidence for the Birch and
  Swinnerton-Dyer conjecture for modular abelian varieties of analytic rank
  zero, Math. Comp. 74 (2005), no. 249, 455-484 (electronic), With
  an appendix by J. Cremona and B. Mazur.
 - ARS06
 - 
A. Agashe, K.A. Ribet and W. Stein, The Manin constant,
to appear in Quarterly J. of Pure and Applied Math. volume in honor of J. Coates.
 - AM69
 - 
M.F. Atiyah and I.G.Macdonald,
Introduction to commutative algebra,
Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., (1969). 
 - BCDT01
 - 
C. Breuil, B. Conrad, F. Diamond, and R. Taylor, On the modularity of
  elliptic curves over 
: wild 3-adic exercises, J. Amer. Math. Soc.
  14 (2001), no. 4, 843-939 (electronic).
 - BCP97
 - 
W. Bosma, J. Cannon, and C. Playoust, The Magma algebra system. I.
  The user language, J. Symbolic Comput. 24 (1997), no. 3-4,
  235-265, Computational algebra and number theory (London, 1993).
 - CW06
 - 
M.Ciperiani, A.Wiles, Solvable points on genus one curves, 
preprint (2006). 
 - CFK06
 - 
C.David, J.Fearnly, H.Kisilevsky, 
Vanishing of twisted 
-functions of elliptic curves, to appear in Experiment. Math. 
 - CM00
 - 
J.E. Cremona and B. Mazur, Visualizing elements in the
  Shafarevich-Tate group, Experiment. Math. 9 (2000), no. 1,
  13-28.
 - CV92
 - 
R.F. Coleman, J.F. Voloch, 
	Companion forms and Kodaira-Spencer theory,
	Invent. Math., 110, (1992), 2, 263-281. 
 - CS01
 - 
	B.Conrad, W.A. Stein,
	Component groups of purely toric quotients,
	Math. Res. Lett., 8, 5-6, (2001), 745-766. 
 - Cre
 - 
	J.E. Cremona, Tables of Elliptic Curves,
		  http://www.maths.nott.ac.uk/personal/jec/ftp/data/
 - CR62
 - 
C.W. Curtis and I. Reiner, Representation theory of finite
  groups and associative algebras, Interscience Publishers, a division of John
  Wiley & Sons, New York-London, 1962, Pure and Applied Mathematics, Vol. XI.
 - Fal86
 - 
G. Faltings, Finiteness theorems for abelian varieties over number
  fields, Arithmetic geometry (Storrs, Conn., 1984), Springer, New York, 1986,
  Translated from the German original [Invent. Math. 73 (1983), no. 3,
  349-366; ibid. 75 (1984), no. 2, 381] by Edward Shipz, pp. 9-27.
 - Ka81
 - 
N.M. Katz, Galois properties of torsion points on abelian varieties,
Invent. Math. 62 (1981), no. 3, 481-502.
 - Kle01
 - 
T. Klenke, Modular Varieties and Visibility, Ph.D. thesis, Harvard
  University (2001).
 - KS00
 - 
D.R. Kohel and W.A. Stein,
Component Groups of Quotients of 
, 
Proc. ANTS-IV, Springer, 2000. 
 - KL89
 - 
V.A. Kolyvagin and D.Y. Logachev, Finiteness of
  the Shafarevich-Tate group and the group of rational
  points for some modular abelian varieties, Algebra i Analiz 1
  (1989), no. 5, 171-196.
 - Maz77
 - 
B.Mazur, Modular curves and the Eisenstein ideal, 
Inst. Hautes Études Sci. Publ. Math., 47, (1977), 33-186. 
 - Maz99
 - 
to3em, Visualizing elements of order three in the Shafarevich-Tate
  group, Asian J. Math. 3 (1999), no. 1, 221-232, Sir Michael
  Atiyah: a great mathematician of the twentieth century.
 - Mil72
 - 
J.S. Milne, On the arithmetic of abelian varieties, Invent.
  Math. 17 (1972), 177-190.
 - Mil86
 - 
to3em, Arithmetic duality theorems, Academic Press Inc., 
Boston, Mass., (1986), x+421. 
 - Rib83
 - 
K.A. Ribet, Congruence relations between modular forms, 
Proc. International Congress of Mathematicians, 503-514, (1983).
 - Rib87
 - 
to3em, On the component groups and the Shimura subgroup of 
,
	Séminaire de Théorie des Nombres, 1987-1988 (Talence, 1987-1988), Exp. No. 6, 10,
	Univ. Bordeaux I.
 - Rib90a
 - 
to3em, On modular representations of 
 arising from modular forms,
Invent. Math., 100 1990, no. 2, 431-476. 
 - Rib90b
 - 
to3em, Raising the levels of modular representations, Séminaire de
  Théorie des Nombres, Paris 1987-88, Birkhäuser Boston, Boston, MA, 1990,
  pp. 259-271.
 - Rib91
 -  
to3em, Lowering the levels of modular representations without multiplicity one,
International Mathematics Research Notices, (1991), 15-19.
 - Rib92
 - 
to3em, Abelian varieties over 
 and modular forms, Algebra
and topology 1992 (Taejon), Korea Adv. Inst. Sci. Tech., Taejon, 1992, pp. 53-79.
 - RS01
 - 
K.A. Ribet and W.A. Stein,
Lectures on Serre's conjectures,
Arithmetic algebraic geometry (Park City, UT, 1999),
IAS/Park City Math. Ser., 9, 143-232, Amer. Math. Soc., Providence, RI, (2001).
 - Rub89
 - 
K.Rubin, 
The work of Kolyvagin on the arithmetic of elliptic curves, 
Arithmetic of complex manifolds (Erlangen, 1988), 128-136, Springer, Berlin, (1989). 
 - Se79
 - 
J-P.Serre, Local fields, Springer-Verlag, New York, (1979).
 - Shi94
 - 
G.Shimura, Introduction to the arithmetic theory of automorphic 
functions, reprint of the 1971 original, Kan Memorial Lectures, 1, 
Princeton University Press, (1994). 
 - Ste00
 - 
W.A. Stein, Explicit approaches to modular abelian varieties, 
Ph.D. thesis, University of California, Berkeley (2000). 
 - Ste04
 - 
W.A. Stein, Shafarevich-Tate Groups of Nonsquare
  Order, Modular Curves and Abelian Varieties, Progress of Mathematics
  (2004), 277-289.
 - Stu87
 - 
J.Sturm, On the congruence of modular forms, Number theory (New York, 1984-1985), 
Springer, Berlin (1987), 275-280. 
 - Wil95
 - 
A.J. Wiles, Modular elliptic curves and Fermat's last theorem,
Ann. of Math. (2), 141(3), (1995), 443-551. 
 
1000
William Stein
2006-06-21