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Rank 0 Quadratic Twists of a Family of Elliptic Curves

Published online by Cambridge University Press:  04 December 2007

Gang Yu
Gang Yu
Affiliation:
Department of Mathematics, The University of Michigan, Ann Arbor, MI 48105 U.S.A e-mail: gangyu@math.lsa.umich.edu
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Abstract

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In this paper, we consider a family of elliptic curves over ${\open Q}$ with 2-torsion part ${\open Z}_2$. We prove that, for every such elliptic curve, a positive proportion of quadratic twists have Mordell–Weil rank 0.

Keywords

elliptic curves2-descent procedurecharacter sums
Type
Research Article
Information
Compositio Mathematica , Volume 135 , Issue 3 , February 2003 , pp. 331 - 356
Copyright
© 2003 Kluwer Academic Publishers