no. 1-2
Bounds for the order of the Tate-Shafarevich group
Compositio Mathematica, Tome 97 (1995) no. 1-2, pp. 71-87. 
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Goldfeld, Dorian; Szpiro, Lucien. Bounds for the order of the Tate-Shafarevich group. Compositio Mathematica, Tome 97 (1995) no. 1-2, pp. 71-87. http://www.numdam.org/item/CM_1995__97_1-2_71_0/

1 Birch, B.J. and Swinnerton-Dyer, H.P.F.: Elliptic curves and modular functions, in Modular Functions of One Variable IV, Lecture Notes in Math. 476, Springer-Verlag, 1975, pp. 2-32. | MR

2 Brumer, A.: The average rank of elliptic curves I, Invent. Math. 109 (1992), 445-472. | MR | Zbl

3 Deligne, P.: La conjecture de Weil 1, Publ. Math. IHES 43 (1974), 273-307. | Numdam | MR | Zbl

4 Flexor, H. and Oesterle, J.: Points de torsion des courbes elliptiques, in L. Szpiro (ed.), Pinceaux de Courbes Elliptiques, Asterisque 183 (1990), 25-36. | Numdam | Zbl

5 Goldfeld, D.: Modular elliptic curves and diophantine problems, in Number Theory, Proc. Conf. of the Canad. Number Theory Assoc., Banff, C Alberta, Canada, 1988, pp. 157-176. | MR | Zbl

6 Gross, B.H.: Kolyvagin's work on elliptic curves, in L-functions and Arithmetic, Proc. of the Durham Symp., 1989, pp. 235-256. | MR | Zbl

7 Hindry, M. and Silverman, J.H.: The canonical height and integral points on elliptic curves, Invent. Math. 93 (1988), 419-450. | MR | Zbl

8 Kolyvagin, V.A.: Finiteness of E(Q) and III(E/Q) for a class of Weil curves, Izv. Akad. Nauk SSSR 52 (1988). | Zbl

9 Kohnen, W. and Zagier, D.B.: Values of L-series of modular forms at the centre of the critical strip, Invent. Math. 64 (1981), 175-198. | MR | Zbl

10 Lang, S.: Conjectured diophantine estimates on elliptic curves, in Arithmetic and Geometry, Papers dedicated to I.R. Shafarevich on the occasion of his sixtieth birthday, Vol. I, Arithmetic, Birkhäuser, 1983, pp. 155-172. | MR | Zbl

11 Mazur, B.: Modular curves and the Eisenstein ideal, IHES Publ. Math. 47 (1977), 33-186. | Numdam | MR | Zbl

12 Milne, J.S.: On a conjecture of Artin and Tate, Annals of Math. 102 (1975), 517-533. | MR | Zbl

13 Pesenti, J. and Szpiro, L.: Discriminant et conducteur des courbes elliptiques non semi-stable, à paraitre.

14 Rubin, K.: Elliptic curves with complex multiplication and the conjecture of Birch and Swinnerton-Dyer, Invent. Math. 64 (1981), 455-470. | MR | Zbl

15 Silverman, J.: The Arithmetic of Elliptic Curves, Graduate Texts in Math. 106, Springer-Verlag, 1986. | MR | Zbl

16 Szpiro, L.: Propriétés numériques du faisceau dualisant relatif, in Pinceaux de Courbes de Genre au Moins Deux, Asterisque 86 (1981), 44-78. | Zbl

17 Szpiro, L.: Discriminant et conducteur, in Seminaire sur les Pinceaux de Courbes Elliptiques, Asterisque 183 (1990), 7-17. | Numdam | MR | Zbl

18 Tate, J.: An algorithm for determining the type of a singular fiber in an elliptic pencil, in Modular Functions of One Variable IV, Lecture Notes in Math. 476, Springer-Verlag, 1975, pp. 33-52. | MR

19 Tate, J.: On a conjecture of Birch and Swinnerton-Dyer and a geometric analogue, Seminaire N. Bourbaki, Exposé 306, 1966. | Numdam | Zbl

20 Taylor, R. and Wiles, A.: Ring theoretic properties of certain Hecke algebras, to appear. | Zbl

21 Titchmarsh, E.C.: The Theory of Functions, 2nd edn., Oxford University Press, Oxford, 1939. | JFM

22 Voloch, F.: On the conjectures of Mordell and Lang in positive characteristic, Inventiones Math. 104 (1991), 643-646. | MR | Zbl

23 Weil, A.: Basic Number Theory, Springer-Verlag, 1967. | MR | Zbl

24 Wiles, A.: Modular elliptic curves and Fermat's last theorem, to appear. | Zbl