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arXiv · 2212.11635

Rational points on rank 2 genus 2 bielliptic curves in the LMFDB

Francesca Bianchi·Oana Padurariu
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Abstract

Building on work of Balakrishnan, Dogra, and of the first author, we provide some improvements to the explicit quadratic Chabauty method to compute rational points on genus $2$ bielliptic curves over $\mathbb{Q}$, whose Jacobians have Mordell-Weil rank equal to $2$. We complement this with a precision analysis to guarantee correct outputs. Together with the Mordell-Weil sieve, this bielliptic quadratic Chabauty method is then the main tool that we use to compute the rational points on the $411$ locally solvable curves from the LMFDB which satisfy the aforementioned conditions.

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Francesca Bianchi, Oana Padurariu. 2022-12-22. Rational points on rank 2 genus 2 bielliptic curves in the LMFDB. https://arxiv.org/abs/2212.11635

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