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    Quadratic Chabauty for modular curves: algorithms and examples

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    Date Issued
    2021
    Author(s)
    Balakrishnan, Jennifer
    Dogra, Netan
    Mueller, J. Steffen
    Tuitman, Jan
    Vonk, Jan
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    Permanent Link
    https://hdl.handle.net/2144/42779
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    First author draft
    Citation (published version)
    Jennifer Balakrishnan, Netan Dogra, J Steffen Mueller, Jan Tuitman, Jan Vonk. "Quadratic Chabauty for modular curves: Algorithms and examples." https://arxiv.org/abs/2101.01862
    Abstract
    We describe how the quadratic Chabauty method may be applied to determine the set of rational points on modular curves of genus g whose Jacobians have Mordell–Weil rank g. This extends our previous work on the split Cartan curve of level 13 and allows us to consider modular curves that may have few known rational points or nontrivial local height contributions away from our working prime. We illustrate our algorithms with a number of examples where we determine the set of rational points on several modular curves of genus 2 and 3: this includes Atkin–Lehner quotients X^+_0 (N) of prime level N, the curve X_S4 (13), as well as a few other curves relevant to Mazur’s Program B.
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    • CAS: Mathematics & Statistics: Scholarly Works [333]
    • BU Open Access Articles [4757]


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