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An infinite family of elliptic curves over Q with large rank via Néron's method

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References

  • [DP] Demazure, M., Pinkham, H., Teissier, B.: Séminaire sur les Singularités des Surfaces. (Lect. Notes Math. vol. 777) Berlin Heidelberg New York: Springer 1980

    Google Scholar 

  • [F] Fried, M.: Construction arising from Néron's high rank curves. Trans. Am. Math. Soc.281, 615–631 (1984)

    Google Scholar 

  • [M] Manin, Ju.: Cubic Forms, 2nd ed., Amsterdam: North-Holland (1986)

    Google Scholar 

  • [N1] Néron, A.: Propriétés arithmétiques de certaines familles de courbes algébriques. Proc. Int. Cong. Math., 1954, Amsterdam, vol. III, pp. 481–488

    Google Scholar 

  • [N2] Néron, A.: Modèles minimaux des variétés abéliennes sur les corps locaux et globaux. Publ. Math., Inst. Hautes Étud. Sci.21 (1964)

  • [Se] Serre, J.-P.: Lectures on the Mordell-Weil Theorem. Braunschweig: Vieweg (1989)

    Google Scholar 

  • [S1] Shioda, T.: Mordell-Weil lattices and Galois representation, I, II, III. Proc. Japan Acad.65A, 268–271; 296–299; 300–303 (1989)

    Google Scholar 

  • [S2] Shioda, T.: On the Mordell-Weil lattices. Comment. Math. Univ. St. Pauli39, 211–240 (1990)

    Google Scholar 

  • [S3] Shioda, T.: Construction of elliptic curves with high rank via the invariants of the Weyl groups. Rikkyo University (Preprint 1990)

  • [Si1] Silverman, J.: Heights and the specialization map for families of abelian varieties. J. Reine Angew Math.342, 197–211 (1983)

    Google Scholar 

  • [Si2] Silverman, J.: The Arithmetic of Elliptic Curves. Berlin Heidelberg New York: Springer 1986

    Google Scholar 

  • [T] Tate, J.: Variation of the canonical height of a point depending on a parameter. Am. J. Math.105, 287–294 (1983)

    Google Scholar 

  • [To] Top, J.: Néron's proof of the existence of elliptic curves overQ with rank at least 11. University Utrecht (Preprint 1987)

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  1. Department of Mathematics, Rikkyo University, Nishi-Ikebukuo, Tokyo 171, Japan

    Tetsuji Shioda

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  1. Tetsuji Shioda
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Oblatum 10-XII-1990

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Shioda, T. An infinite family of elliptic curves over Q with large rank via Néron's method. Invent Math 106, 109–119 (1991). https://doi.org/10.1007/BF01243907

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