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

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

22 Dec 2022arXiv:2212.11635links table onlyarchive 2025-07-28

Francesca Bianchi, Oana Padurariu

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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 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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bianchifrancesca/qc_bielliptic officialmentioned in paper report
oana-adascalitei/mwsievefordatabase officialmentioned in paper report

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