Quadratic Chabauty Experiments on Genus 2 Bielliptic Modular Curves in the LMFDB
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912607355535360 |
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| author | Finnerty, Kate |
| author_facet | Finnerty, Kate |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_03784 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quadratic Chabauty Experiments on Genus 2 Bielliptic Modular Curves in the LMFDB Finnerty, Kate Number Theory 11D45, 11Y50 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. |
| title | Quadratic Chabauty Experiments on Genus 2 Bielliptic Modular Curves in the LMFDB |
| topic | Number Theory 11D45, 11Y50 |
| url | https://arxiv.org/abs/2507.03784 |