Mathematika

Table of Contents - December 2005 - Volume 52, Issue 1-2  

Research Article

On the Quadratic Twists of a Family of Elliptic Curves

Professor Gang Yua1

a1 Department of Mathematics, University of Michigan, 525 E. University Ave., Ann Arbor, MI 48109–1109, USA. E-mail: gangyu@math.lsa.umich.edu.

Abstract

In this paper is considered the average size of the 2-Selmer groups of a class of quadratic twists of each elliptic curve over with -torsion group 2 × 2. The existence is shown of a positive proportion of quadratic twists of such a curve, each of which has rank 0 Mordell-Weil group.

(Received May 10 2003)

MSC (2000)

  • Primary, 14H52;
  • Secondary, 11G05