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Estimating isogenies on elliptic curves

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References

  • [AM] Anderson, M., Masser, D.W.: Lower bounds for heights on elliptic curves. Math. Z.174, 23–34 (1980)

    Google Scholar 

  • [Ba] Baker, A.: On the periods of the Weierstrass ℘-function. Symposia Math. Vol. IV, INDAM Rome 1968, Academic Press, London 1970, pp. 155–174

    Google Scholar 

  • [BM] Brownawell, W.D., Masser, D.W.: Multiplicity estimates for analytic functions I. J. Reine Angew. Math.314, 200–216 (1979)

    Google Scholar 

  • [Ca] Cassels, J.W.S.: An introduction to the geometry of numbers. Berlin Göttingen Heidelberg: Springer 1959

    Google Scholar 

  • [CC] Chudnovsky, D.V., Chudnovsky, G.V.: Padé approximations and algebraic geometry. Proc. Natl. Acad. Sci. USA82, 2212–2216 (1985)

    Google Scholar 

  • [FP] Faisant, A., Philibert, G.: Quelques résultats de transcendance liés á l'invariant modulairej. J. Number Theory25, 184–200 (1987)

    Google Scholar 

  • [K] Kolchin, E.R.: Algebraic groups and algebraic dependence. Am. J. Math.90, 1151–1164 (1968)

    Google Scholar 

  • [La] Laurent, M.: Une nouvelle démonstration du théorème d'isogénie, d'après D.V. et G.V. Choodnovsky, Séminaire de Théorie de Nombres de Paris 1985–6, Boston Basel Stuttgart, Birkhäuser, 1987, pp. 119–131

    Google Scholar 

  • [Lo] Loxton, J.H.: Some problems involving powers of integers. Acta Arith.46, 113–123 (1986)

    Google Scholar 

  • [M] Masser, D.W.: Counting points of small height on elliptic curves. Bull. Soc. Math. Fr. (to appear)

  • [MW1] Masser, D.W., Wüstholz, G.: Fields of large transcendence degree generated by values of elliptic functions. Invent. Math.72, 407–464 (1983)

    Google Scholar 

  • [MW2] Masser, D.W., Wüstholz, G.: Zero estimates on group varieties II. Invent. Math.80, 233–267 (1985)

    Google Scholar 

  • [MW3] Masser, D.W., Wüstholz, G.: Some effective estimates for elliptic curves, to appear in the Proceedings of the 1988 Erlangen Workshop on Arithmetic Complex Manifolds. (Lect. Notes Math., Berlin Heidelberg New York: Springer, to appear)

  • [P] Philippon, P.: Lemmes de zéros dans les groupes algébriques. Bull. Soc. Math. Fr.114, 355–383 (1986)

    Google Scholar 

  • [S] Silverman, J.H.: The arithmetic of elliptic curves. New York Berlin Heidelberg: Springer 1986

    Google Scholar 

  • [V] Vélu, J.: Isogénies entre coubes elliptiques. C.R. Acad. Sci. Paris A273, 238–241 (1973)

    Google Scholar 

  • [Wa] Waldschmidt, M.: Nombres transcendants et groupes algébriques. Astérisque69–70 (1979)

  • [Wü 1] Wüstholz, G.: Multiplicity estimates on group varieties. Ann. Math.129, 471–500 (1989)

    Google Scholar 

  • [Wü 2] Wüstholz, G.: Zum Periodenproblem. Invent. Math.78, 381–391 (1984)

    Google Scholar 

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Masser, D.W., Wüstholz, G. Estimating isogenies on elliptic curves. Invent Math 100, 1–24 (1990). https://doi.org/10.1007/BF01231178

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