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
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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