Explicit Chabauty-Kim for the split Cartan modular curve of level 13

DOI10.4007/ANNALS.2019.189.3.6zbMATH Open1469.14050arXiv1711.05846OpenAlexW2962817287WikidataQ127856263 ScholiaQ127856263MaRDI QIDQ2320603

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Publication date: 23 August 2019

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Abstract: We extend the explicit quadratic Chabauty methods developed in previous work by the first two authors to the case of non-hyperelliptic curves. This results in an algorithm to compute the rational points on a curve of genus $gge2$ over the rationals whose Jacobian has Mordell-Weil rank $g$ and Picard number greater than one, and which satisfies some additional conditions. This algorithm is then applied to the modular curve $X_s(13)$, completing the classification of non-CM elliptic curves over $mathbfQ$ with split Cartan level structure due to Bilu-Parent and Bilu-Parent-Rebolledo.

Full work available at URL: https://arxiv.org/abs/1711.05846

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