Bibliography

BCDT01
C. Breuil, B. Conrad, Fred Diamond, and R. Taylor, On the modularity of elliptic curves over $\bold Q$: wild 3-adic exercises, J. Amer. Math. Soc. 14 (2001), no. 4, 843-939 (electronic). MR 2002d:11058

Bir71
B.J. Birch, Elliptic curves over ${\mathbf{Q}}$: 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.

Coh00
Henri Cohen, Advanced topics in computational number theory, Graduate Texts in Mathematics, vol. 193, Springer-Verlag, New York, 2000. MR MR1728313 (2000k:11144)

Cp86
J.W.S. Cassels and A. Fröhlich (eds.), Algebraic number theory, London, Academic Press Inc. [Harcourt Brace Jovanovich Publishers], 1986, Reprint of the 1967 original.

Cre97
J.E. Cremona, Algorithms for modular elliptic curves, second ed., Cambridge University Press, Cambridge, 1997,
http://www.maths.nott.ac.uk/personal/jec/book/.

CS00
J. Coates and R. Sujatha, Galois cohomology of elliptic curves, Tata Institute of Fundamental Research Lectures on Mathematics, 88, Published by Narosa Publishing House, New Delhi, 2000. MR MR1759312 (2001b:11046)

Dok04
Tim Dokchitser, Computing special values of motivic $L$-functions, Experiment. Math. 13 (2004), no. 2, 137-149.

Elk87
Noam D. Elkies, The existence of infinitely many supersingular primes for every elliptic curve over ${\bf Q}$, Invent. Math. 89 (1987), no. 3, 561-567. MR MR903384 (88i:11034)

GJP+05
G. Grigorov, A. Jorza, S. Patrikis, C. Patrascu, and W. Stein, Verification of the Birch and Swinnerton-Dyer Conjecture for Specific Elliptic Curves, (Submitted)
http://www.wstein.org/papers/bsdalg/ (2005).

Gro91
B.H. Gross, Kolyvagin's work on modular elliptic curves, $L$-functions and arithmetic (Durham, 1989), Cambridge Univ. Press, Cambridge, 1991, pp. 235-256.

Kol91
V. A. Kolyvagin, On the structure of Selmer groups, Math. Ann. 291 (1991), no. 2, 253-259. MR 93e:11073

LT58
S. Lang and J. Tate, Principal homogeneous spaces over abelian varieties, Amer. J. Math. 80 (1958), 659-684.

Maz78
B. Mazur, Rational isogenies of prime degree (with an appendix by D. Goldfeld), Invent. Math. 44 (1978), no. 2, 129-162.

MST06
Barry Mazur, William Stein, and John Tate, Computation of $p$-adic heights and log convergence, Doc. Math. (2006), no. Extra Vol., 577-614 (electronic). MR MR2290599

MT91
B. Mazur and J. Tate, The $p$-adic sigma function, Duke Math. J. 62 (1991), no. 3, 663-688. MR 93d:11059

MTT86
B. Mazur, J. Tate, and J. Teitelbaum, On $p$-adic analogues of the conjectures of Birch and Swinnerton-Dyer, Invent. Math. 84 (1986), no. 1, 1-48.

Ser72
J-P. Serre, Propriétés galoisiennes des points d'ordre fini des courbes elliptiques, Invent. Math. 15 (1972), no. 4, 259-331.

Ser79
to3em, Local fields, Springer-Verlag, New York, 1979, Translated from the French by Marvin Jay Greenberg.

Ser97
to3em, Galois cohomology, Springer-Verlag, Berlin, 1997, Translated from the French by Patrick Ion and revised by the author.

Sil92
J.H. Silverman, The arithmetic of elliptic curves, Springer-Verlag, New York, 1992, corrected reprint of the 1986 original.

Ste02
W.A. Stein, There are genus one curves over $\mathbf{Q}$ of every odd index, J. Reine Angew. Math. 547 (2002), 139-147. MR 2003c:11059

SW07
William Stein and Chris Wuthrich, Computations About Tate-Shafarevich Groups Uusing Iwasawa Theory, In preparation (2007).

Wil95
A.J. Wiles, Modular elliptic curves and Fermat's last theorem, Ann. of Math. (2) 141 (1995), no. 3, 443-551. MR 1333035 (96d:11071)

Wil00
to3em, The Birch and Swinnerton-Dyer Conjecture,
http://www.claymath.org/prize_problems/birchsd.htm.



William 2007-05-25