On ranks of twists of elliptic curves and power-free values of binary forms
Journal of the American Mathematical Society, Tome 08 (1995) no. 4, pp. 943-973

Voir la notice de l'article provenant de la source American Mathematical Society

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Stewart, C. L.; Top, J. On ranks of twists of elliptic curves and power-free values of binary forms. Journal of the American Mathematical Society, Tome 08 (1995) no. 4, pp. 943-973. doi: 10.1090/S0894-0347-1995-1290234-5

[1] Stienstra, Jan, Beukers, Frits On the Picard-Fuchs equation and the formal Brauer group of certain elliptic 𝐾3-surfaces Math. Ann. 1985 269 304

[2] Birch, B. J., Stephens, N. M. The parity of the rank of the Mordell-Weil group Topology 1966 295 299

[3] Birch, B. J., Swinnerton-Dyer, H. P. F. Notes on elliptic curves. I J. Reine Angew. Math. 1963 7 25

[4] Birch, B. J., Swinnerton-Dyer, H. P. F. Notes on elliptic curves. II J. Reine Angew. Math. 1965 79 108

[5] Swinnerton-Dyer, H. P. F., Birch, B. J. Elliptic curves and modular functions 1975 2 32

[6] Brumer, Armand The average rank of elliptic curves. I Invent. Math. 1992 445 472

[7] Brumer, Armand, Mcguinness, Oisã­N The behavior of the Mordell-Weil group of elliptic curves Bull. Amer. Math. Soc. (N.S.) 1990 375 382

[8] Craig, Maurice A type of class group for imaginary quadratic fields Acta Arith. 1973

[9] Craig, Maurice A construction for irregular discriminants Osaka Math. J. 1977 365 402

[10] Frey, G. On the Selmer group of twists of elliptic curves with 𝑄-rational torsion points Canad. J. Math. 1988 649 665

[11] Fried, M. Constructions arising from Néron’s high rank curves Trans. Amer. Math. Soc. 1984 615 631

[12] Goldfeld, Dorian Conjectures on elliptic curves over quadratic fields 1979 108 118

[13] Gouvãªa, F., Mazur, B. The square-free sieve and the rank of elliptic curves J. Amer. Math. Soc. 1991 1 23

[14] Greaves, George Power-free values of binary forms Quart. J. Math. Oxford Ser. (2) 1992 45 65

[15] Hardy, G. H., Wright, E. M. An introduction to the theory of numbers 1979

[16] Honda, Taira Isogenies, rational points and section points of group varieties Jpn. J. Math. 1960 84 101

[17] Hooley, C. On the power free values of polynomials Mathematika 1967 21 26

[18] Hooley, C. Applications of sieve methods to the theory of numbers 1976

[19] Igusa, Jun-Ichi Arithmetic variety of moduli for genus two Ann. of Math. (2) 1960 612 649

[20] Kramer, Kenneth Arithmetic of elliptic curves upon quadratic extension Trans. Amer. Math. Soc. 1981 121 135

[21] Kramer, K., Tunnell, J. Elliptic curves and local 𝜖-factors Compositio Math. 1982 307 352

[22] Lagarias, J. C., Odlyzko, A. M. Effective versions of the Chebotarev density theorem 1977 409 464

[23] Mahler, Kurt Zur Approximation algebraischer Zahlen. I Math. Ann. 1933 691 730

[24] Mahler, Kurt Zur Approximation algebraischer Zahlen. III Acta Math. 1933 91 166

[25] Mai, Liem The analytic rank of a family of elliptic curves Canad. J. Math. 1993 847 862

[26] Mestre, Jean-Franã§Ois Courbes elliptiques et groupes de classes d’idéaux de certains corps quadratiques J. Reine Angew. Math. 1983 23 35

[27] Mestre, Jean-Franã§Ois Rang de courbes elliptiques d’invariant donné C. R. Acad. Sci. Paris Sér. I Math. 1992 919 922

[28] Mestre, Jean-Franã§Ois Courbes elliptiques de rang ≥12 sur 𝑄(𝑡) C. R. Acad. Sci. Paris Sér. I Math. 1991 171 174

[29] Mordell, L. J. Diophantine equations 1969

[30] Nakano, Shin Construction of pure cubic fields with large 2-class groups Osaka J. Math. 1988 161 170

[31] Nã©Ron, A. Propriétés arithmétiques de certaines familles de courbes algébriques 1956 481 488

[32] Schneiders, U., Zimmer, H. G. The rank of elliptic curves upon quadratic extension 1991 239 260

[33] Schoen, Chad Bounds for rational points on twists of constant hyperelliptic curves J. Reine Angew. Math. 1990 196 204

[34] Schoof, R. J. Class groups of complex quadratic fields Math. Comp. 1983 295 302

[35] Serre, Jean-Pierre Lectures on the Mordell-Weil theorem 1989

[36] Shioda, Tetsuji An infinite family of elliptic curves over 𝑄 with large rank via Néron’s method Invent. Math. 1991 109 119

[37] Silverman, Joseph H. Heights and the specialization map for families of abelian varieties J. Reine Angew. Math. 1983 197 211

[38] Silverman, Joseph H. Divisibility of the specialization map for families of elliptic curves Amer. J. Math. 1985 555 565

[39] Stewart, C. L. On the number of solutions of polynomial congruences and Thue equations J. Amer. Math. Soc. 1991 793 835

[40] Tate, J. Algorithm for determining the type of a singular fiber in an elliptic pencil 1975 33 52

[41] Zagier, D., Kramarz, G. Numerical investigations related to the 𝐿-series of certain elliptic curves J. Indian Math. Soc. (N.S.) 1987

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