Rank zero quadratic twists of modular elliptic curves
Compositio Mathematica, Tome 104 (1996) no. 3, pp. 293-304.
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     title = {Rank zero quadratic twists of modular elliptic curves},
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     pages = {293--304},
     publisher = {Kluwer Academic Publishers},
     volume = {104},
     number = {3},
     year = {1996},
     mrnumber = {1424558},
     zbl = {0876.11025},
     language = {en},
     url = {http://archive.numdam.org/item/CM_1996__104_3_293_0/}
}
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Ono, Ken. Rank zero quadratic twists of modular elliptic curves. Compositio Mathematica, Tome 104 (1996) no. 3, pp. 293-304. http://archive.numdam.org/item/CM_1996__104_3_293_0/

1 Bump, D., Friedberg, S. and Hoffstein J.: Nonvanishing theorems for L-functions of modular fomrs and their derivatives, Inventiones Math. 102 (1990), 543-618. | MR | Zbl

2 Deligne, P.: La conjecture de Weil I, Publ. Math. I.H.E.S. 43 (1974), 273-307. | Numdam | MR | Zbl

3 Diamond, F. and Kramer, K.: Modularity of a family of elliptic curves, Math. Research Letters (2)(3) (1995), 299-304. | MR | Zbl

4 Gouvêa, F. and Mazur, B.: The square-free sieve and the rank of elliptic curves, J. Amer. Math. Soc. 4 (1991), 1-23. | MR | Zbl

5 Husemöller, D.: Elliptic curves, Springer-Verlag, New York, 1987. | MR | Zbl

6 Knapp, A.: Elliptic curves, Princeton Univ. Press, 1992. | MR | Zbl

7 Koblitz, N.: Introduction to elliptic curves and modular forms, Springer-Verlag, 1984. | MR | Zbl

8 Kohnen, W.: A remark on the Shimura correspondence, Glasgow Math. J. 30 (1988), 285-291. | MR | Zbl

9 Kolyvagin, V.A.: Finiteness of E(Q) and the Tate-Shafarevich group of E(Q) for a subclass of Weil curves (Russian), Izv. Akad. Nauk, USSR, ser. Matem. 52 (1988). | Zbl

10 Lieman, D.: Nonvanishing of L-series associated to cubic twists of elliptic curves, Jour Annals of Math. 40 (1994), 81-108. | MR | Zbl

11 Mai, L. and Murty, M.R.: A note on quadratric twists of an elliptic curve, Elliptic curves and related topics, Ed. H. Kisilevsky and M. R. Murty, Amer. Math. Soc. [CRM Proceedings and Lecture Notes] (1994), 121-124. | MR | Zbl

12 Murty, M.R. and Murty, V.K.: Mean values of derivatives of modular L-series, Annals of Math. 133 (1991) 447-475. | MR | Zbl

13 Ono, K.: Euler's concordant forms, Acta. Arith., to appear. | Zbl

14 Silverman, J.: The arithmetic of elliptic curves, Springer-Verlag, New York, 1986. | MR | Zbl

15 Shimura, G.: On modular forms of half-integral weight, Annals of Math. 97 (1973), 440-481. | MR | Zbl

16 Stewart, C.L. and Top, J.: On ranks of twists of elliptic curves and power-free values of binary forms, preprint. | Zbl

17 Tunnell, J.: A classical Diophantine problem and modular forms of weight 3/2, Inventiones Math. 72 (1983), 323-334. | MR | Zbl

18 Vignéras, M.-F.: Facteurs gamma et equations fonctionelles, Springer Lect. in Math. 627 (1977), 79-103. | MR | Zbl

19 Waldspurger, J.L.: Sur les coefficients de Fourier des formes modulaires de poids demi-entier, J. Math. Pures et Appl. 60 (1981), 375-484. | MR | Zbl

20 Wiles, A.: Modular elliptic curves and Fermat's Last Theorem, Ann. Math. 141(3) (1995), 443-551. | MR | Zbl