Computation of the Selmer groups of certain parametrized elliptic curves

• Autorzy: S. Schmitt
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1996-1997
• Tom: 78
• Numer: 3
• Strony: 241-254

Daty

wydano

1997

otrzymano

1995-10-24

poprawiono

1996-08-27

Twórcy

autor

S. Schmitt

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

Bibliografia

• [MF IV] B. J. Birch and W. Kuyk, Modular Functions of One Variable IV, Lecture Notes in Math. 476, Springer, 1975.
• [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.
• [Fo] H. G. Folz, Ein Beschränktheitssatz für die Torsion von 2-defizienten elliptischen Kurven über algebraischen Zahlkörpern, Dissertation, Universität des Saarlandes, 1985.
• [H-M] T. Honda and I. Miyawaki, Zeta-functions of elliptic curves of 2-power conductor, J. Math. Soc. Japan 26 (1974), 362-373.
• [Ko] N. Koblitz, Introduction to Elliptic Curves and Modular Forms, Springer, New York, 1984.
• [Og] A. Ogg, Abelian curves over 2-power conductor, to appear.
• [Sc] S. Schmitt, Berechnung der Mordell-Weil Gruppe parametrisierter elliptischer Kurven, Diplomarbeit, Universität des Saarlandes, 1995.
• [Si] J. H. Silverman, The difference between the Weil height and the canonical height on elliptic curves, Math. Comp. 55 (1990), 723-743.
• [Si-Ta] J. H. Silverman and J. Tate, Rational Points on Elliptic Curves, Springer, 1985.
• [S-T] R. J. Stroeker and J. Top, On the equation Y² = (X+p)(X²+p²), Rocky Mountain J. Math. 27 (1994), 1135-1161.
• [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.
• [We] E. Weiss, Algebraic Number Theory, McGraw-Hill, 1963.
• [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.