a1 Department of Mathematics, University of Michigan, 525 E. University Ave., Ann Arbor, MI 48109–1109, USA. E-mail: firstname.lastname@example.org.
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)