Quadratic Chabauty for Atkin–Lehner quotients of modular curves of prime level and genus 4, 5, 6

DOI10.4064/AA220110-7-3arXiv2105.04811OpenAlexW3163116263MaRDI QIDQ6136600

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Publication date: 31 August 2023

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Abstract: We use the method of quadratic Chabauty on the quotients $X_0^{+}(N)$ of modular curves $X_0(N)$ 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 $N=137,173,199,251,311,157,181,227,263,163,197,211,223,269,271,359$.

Full work available at URL: https://arxiv.org/abs/2105.04811

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