ArticleOriginal scientific text

Title

Computation of the Selmer groups of certain parametrized elliptic curves

Authors 1

Affiliations

  1. Fachbereich Mathematik, Universität des Saarlandes, Bau 27, Zimmer 429, D-66041 Saarbrücken, Germany

Bibliography

  1. [MF IV] B. J. Birch and W. Kuyk, Modular Functions of One Variable IV, Lecture Notes in Math. 476, Springer, 1975.
  2. [B-S] B. J. Birch and H. P. F. Swinnerton-Dyer, Elliptic curves and modular functions, in: Modular Functions of One Variable IV, Antwerpen 1972, Lecture Notes in Math. 476, Springer, 1975, 2-32.
  3. [Fo] H. G. Folz, Ein Beschränktheitssatz für die Torsion von 2-defizienten elliptischen Kurven über algebraischen Zahlkörpern, Dissertation, Universität des Saarlandes, 1985.
  4. [H-M] T. Honda and I. Miyawaki, Zeta-functions of elliptic curves of 2-power conductor, J. Math. Soc. Japan 26 (1974), 362-373.
  5. [Ko] N. Koblitz, Introduction to Elliptic Curves and Modular Forms, Springer, New York, 1984.
  6. [Og] A. Ogg, Abelian curves over 2-power conductor, to appear.
  7. [Sc] S. Schmitt, Berechnung der Mordell-Weil Gruppe parametrisierter elliptischer Kurven, Diplomarbeit, Universität des Saarlandes, 1995.
  8. [Si] J. H. Silverman, The difference between the Weil height and the canonical height on elliptic curves, Math. Comp. 55 (1990), 723-743.
  9. [Si-Ta] J. H. Silverman and J. Tate, Rational Points on Elliptic Curves, Springer, 1985.
  10. [S-T] R. J. Stroeker and J. Top, On the equation Y² = (X+p)(X²+p²), Rocky Mountain J. Math. 27 (1994), 1135-1161.
  11. [Ta] J. Tate, Algorithm for determining the type of a singular fiber in an elliptic pencil, in: Modular Functions of One Variable IV, Antwerpen 1972, Lecture Notes in Math. 476, Springer, 1975, 33-52.
  12. [We] E. Weiss, Algebraic Number Theory, McGraw-Hill, 1963.
  13. [Zi] H. G. Zimmer, A limit formula for the canonical height of an elliptic curve and its application to height computations, in: Number Theory, R. Mollin (ed.), Proc. First Conf. Canad. Number Theory Assoc., Banff, 1988, de Gruyter, 1990, 641-659.
Pages:
241-254
Main language of publication
English
Received
1995-10-24
Accepted
1996-08-27
Published
1997
Exact and natural sciences