References
[AM] Anderson, M., Masser, D.W.: Lower bounds for heights on elliptic curves. Math. Z.174, 23–34 (1980)
[Ba] Baker, A.: On the periods of the Weierstrass ℘-function. Symposia Math. Vol. IV, INDAM Rome 1968, Academic Press, London 1970, pp. 155–174
[BM] Brownawell, W.D., Masser, D.W.: Multiplicity estimates for analytic functions I. J. Reine Angew. Math.314, 200–216 (1979)
[Ca] Cassels, J.W.S.: An introduction to the geometry of numbers. Berlin Göttingen Heidelberg: Springer 1959
[CC] Chudnovsky, D.V., Chudnovsky, G.V.: Padé approximations and algebraic geometry. Proc. Natl. Acad. Sci. USA82, 2212–2216 (1985)
[FP] Faisant, A., Philibert, G.: Quelques résultats de transcendance liés á l'invariant modulairej. J. Number Theory25, 184–200 (1987)
[K] Kolchin, E.R.: Algebraic groups and algebraic dependence. Am. J. Math.90, 1151–1164 (1968)
[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
[Lo] Loxton, J.H.: Some problems involving powers of integers. Acta Arith.46, 113–123 (1986)
[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)
[MW2] Masser, D.W., Wüstholz, G.: Zero estimates on group varieties II. Invent. Math.80, 233–267 (1985)
[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)
[S] Silverman, J.H.: The arithmetic of elliptic curves. New York Berlin Heidelberg: Springer 1986
[V] Vélu, J.: Isogénies entre coubes elliptiques. C.R. Acad. Sci. Paris A273, 238–241 (1973)
[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)
[Wü 2] Wüstholz, G.: Zum Periodenproblem. Invent. Math.78, 381–391 (1984)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Masser, D.W., Wüstholz, G. Estimating isogenies on elliptic curves. Invent Math 100, 1–24 (1990). https://doi.org/10.1007/BF01231178
Issue Date:
DOI: https://doi.org/10.1007/BF01231178