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arXiv · 2507.03784

Quadratic Chabauty Experiments on Genus 2 Bielliptic Modular Curves in the LMFDB

Kate Finnerty
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Abstract

We present results of quadratic Chabauty experiments on genus 2 bielliptic modular curves of Jacobian rank 2 that have recently been added to the LMFDB. We apply quadratic Chabauty methods over both the rationals and quadratic imaginary fields. In a number of cases, the experiments yielded algebraic irrational points among the set of mock rational points. We highlight specific notable examples, including the non-split Cartan modular curve $X^+_{ns}(15)$. Lastly, we offer a conjecture relating the level of the modular curve to the potential number fields over which points can arise.

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Kate Finnerty. 2025-07-04. Quadratic Chabauty Experiments on Genus 2 Bielliptic Modular Curves in the LMFDB. https://arxiv.org/abs/2507.03784

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