The behavior of the Mordell-Weil group of elliptic curves
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- by Armand Brumer and Oisín McGuinness PDF
- Bull. Amer. Math. Soc. 23 (1990), 375-382
References
- B. J. Birch and W. Kuyk (eds.), Modular functions of one variable. IV, Lecture Notes in Mathematics, Vol. 476, Springer-Verlag, Berlin-New York, 1975. MR 0376533
- Armand Brumer and Kenneth Kramer, The rank of elliptic curves, Duke Math. J. 44 (1977), no. 4, 715–743. MR 457453 (1977), 715-743.
- Joe P. Buhler, Benedict H. Gross, and Don B. Zagier, On the conjecture of Birch and Swinnerton-Dyer for an elliptic curve of rank $3$, Math. Comp. 44 (1985), no. 170, 473–481. MR 777279, DOI 10.1090/S0025-5718-1985-0777279-X
- H. Davenport and H. Heilbronn, On the density of discriminants of cubic fields. II, Proc. Roy. Soc. London Ser. A 322 (1971), no. 1551, 405–420. MR 491593, DOI 10.1098/rspa.1971.0075
- Dorian Goldfeld, Conjectures on elliptic curves over quadratic fields, Number theory, Carbondale 1979 (Proc. Southern Illinois Conf., Southern Illinois Univ., Carbondale, Ill., 1979) Lecture Notes in Math., vol. 751, Springer, Berlin, 1979, pp. 108–118. MR 564926 6. F. Gouvea and B. Mazur, The square-free sieve and the rank of Mordell-Weil, preprint, April 1989.
- Daniel R. Grayson, The arithogeometric mean, Arch. Math. (Basel) 52 (1989), no. 5, 507–512. MR 998624, DOI 10.1007/BF01198359
- D. Zagier and G. Kramarz, Numerical investigations related to the $L$-series of certain elliptic curves, J. Indian Math. Soc. (N.S.) 52 (1987), 51–69 (1988). MR 989230
- B. Mazur, Modular curves and the Eisenstein ideal, Inst. Hautes Études Sci. Publ. Math. 47 (1977), 33–186 (1978). With an appendix by Mazur and M. Rapoport. MR 488287, DOI 10.1007/BF02684339
- Jean-François Mestre, Formules explicites et minorations de conducteurs de variétés algébriques, Compositio Math. 58 (1986), no. 2, 209–232 (French). MR 844410
- J.-F. Mestre, La méthode des graphes. Exemples et applications, Proceedings of the international conference on class numbers and fundamental units of algebraic number fields (Katata, 1986) Nagoya Univ., Nagoya, 1986, pp. 217–242 (French). MR 891898
- J.-F. Mestre and J. Oesterlé, Courbes de Weil semi-stables de discriminant une puissance $m$-ième, J. Reine Angew. Math. 400 (1989), 173–184 (French). MR 1013729, DOI 10.1515/crll.1989.400.173
- Jordi Quer, Corps quadratiques de $3$-rang $6$ et courbes elliptiques de rang $12$, C. R. Acad. Sci. Paris Sér. I Math. 305 (1987), no. 6, 215–218 (French, with English summary). MR 907945
- Karl Rubin, The work of Kolyvagin on the arithmetic of elliptic curves, Arithmetic of complex manifolds (Erlangen, 1988) Lecture Notes in Math., vol. 1399, Springer, Berlin, 1989, pp. 128–136. MR 1034261, DOI 10.1007/BFb0095973
- Joseph H. Silverman, The arithmetic of elliptic curves, Graduate Texts in Mathematics, vol. 106, Springer-Verlag, New York, 1986. MR 817210, DOI 10.1007/978-1-4757-1920-8
- Joseph H. Silverman, Computing heights on elliptic curves, Math. Comp. 51 (1988), no. 183, 339–358. MR 942161, DOI 10.1090/S0025-5718-1988-0942161-4
- John T. Tate, The arithmetic of elliptic curves, Invent. Math. 23 (1974), 179–206. MR 419359, DOI 10.1007/BF01389745
- Lawrence C. Washington, Number fields and elliptic curves, Number theory and applications (Banff, AB, 1988) NATO Adv. Sci. Inst. Ser. C: Math. Phys. Sci., vol. 265, Kluwer Acad. Publ., Dordrecht, 1989, pp. 245–278. MR 1123077
Additional Information
- Journal: Bull. Amer. Math. Soc. 23 (1990), 375-382
- MSC (1985): Primary 11G40; Secondary 11D25, 11G05, 11-04, 14K15
- DOI: https://doi.org/10.1090/S0273-0979-1990-15937-3
- MathSciNet review: 1044170