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On the Quadratic Twists of a Family of Elliptic Curves

Part of: Arithmetic algebraic geometry Curves

Published online by Cambridge University Press:  21 December 2009

Gang Yu
Gang Yu
Affiliation:
Department of Mathematics, University of Michigan, 525 E. University Ave., Ann Arbor, MI 48109–1109, USA. E-mail: gangyu@math.lsa.umich.edu.
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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 ℚ with ℚ-torsion group ℤ2 × ℤ2. The existence is shown of a positive proportion of quadratic twists of such a curve, each of which has rank 0 Mordell-Weil group.

MSC classification

Secondary: 14H52: Elliptic curves 11G05: Elliptic curves over global fields
Type
Research Article
Information
Mathematika , Volume 52 , Issue 1-2 , December 2005 , pp. 139 - 154
Copyright
Copyright © University College London 2005

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