Papers › Explicit Chabauty-Kim for the Split Cartan Modular Curve of Level 13
Explicit Chabauty-Kim for the Split Cartan Modular Curve of Level 13
Jennifer S. Balakrishnan, Netan Dogra, J. Steffen Müller, Jan Tuitman, Jan Vonk
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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 g ≥2 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 Xₛ(13), completing the classification of non-CM elliptic curves over 𝐐 with split Cartan level structure due to Bilu-Parent and Bilu-Parent-Rebolledo.
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