A Family of Elliptic Curves with a Lower Bound on 2-Selmer Ranks of Quadratic Twists

Zev Klagsbrun

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arXiv · 1201.5407

A Family of Elliptic Curves with a Lower Bound on 2-Selmer Ranks of Quadratic Twists

Zev Klagsbrun

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Abstract

For any number field K with a complex place, we present an infinite family of elliptic curves defined over K such that $dim \mathbb{F}_2 Sel_2(E^F/K) \ge dim \mathbb{F}_2 E^F(K)[2] + r_2$ for every quadratic twist E^F of every curve E in this family, where r_2 is the number of complex places of K. This provides a counterexample to a conjecture appearing in work of Mazur and Rubin.

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BibTeX RIS

Zev Klagsbrun. 2012-10-19. A Family of Elliptic Curves with a Lower Bound on 2-Selmer Ranks of Quadratic Twists. https://arxiv.org/abs/1201.5407

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