Average rank of quadratic twists with a rational point of almost minimal height

Joachim Petit

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arXiv · 2011.13195

Average rank of quadratic twists with a rational point of almost minimal height

Joachim Petit

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Abstract

Given a family of quadratic twists of a fixed elliptic curve defined over $\mathbb{Q}$, we investigate the average rank in the subfamily of twists having a nontorsion rational point of almost minimal height. We show in particular that the average analytic rank is greater than one.

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Joachim Petit. 2020-11-26. Average rank of quadratic twists with a rational point of almost minimal height. https://arxiv.org/abs/2011.13195

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