On the Quadratic Twists of a Family of Elliptic Curves
نویسندگان
چکیده
In this paper, we consider 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. We prove the existence of a positive proportion of quadratic twists of such a curve, each of which has rank 0 Mordell-Weil group.
منابع مشابه
A Note on Twists of (y^2=x^3+1)
‎‎In the category of Mordell curves (E_D:y^2=x^3+D) with nontrivial torsion groups we find curves of the generic rank two as quadratic twists of (E_1), ‎and of the generic rank at least two and at least three as cubic twists of (E_1). ‎Previous work‎, ‎in the category of Mordell curves with trivial torsion groups‎, ‎has found infinitely many elliptic curves with ...
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In this paper, we consider a family of elliptic curves over Q with 2-torsion part Z2. We prove that, for every such elliptic curve, a positive proportion of quadratic twists have Mordell–Weil rank 0. Mathematics Subject Classifications (2000). 11G05, 11L40, 14H52.
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