# Quadratic Chabauty for Atkin-Lehner Quotients of Modular Curves of Prime Level and Genus 4, 5, 6

@inproceedings{Advzaga2021QuadraticCF, title={Quadratic Chabauty for Atkin-Lehner Quotients of Modular Curves of Prime Level and Genus 4, 5, 6}, author={Nikola Advzaga and V. Arul and Lea Beneish and Mingjie Chen and Shiva Chidambaram and Timo Keller and Boya Wen}, year={2021} }

We use the method of quadratic Chabauty on the quotients X 0 (N) of modular curves X0(N) by their Fricke involutions to provably compute all the rational points of these curves for prime levels N of genus four, five, and six. We find that the only such curves with exceptional rational points are of levels 137 and 311. In particular there are no exceptional rational points on those curves of genus five and six. More precisely, we determine the rational points on the curves X 0 (N) for N = 137… Expand

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