Rational points on Atkin-Lehner quotients of geometrically hyperelliptic Shimura curves

DOI10.1016/J.EXMATH.2023.02.005arXiv2212.04553OpenAlexW4327702811MaRDI QIDQ6056567

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Publication date: 2 October 2023

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Abstract: Guo and Yang give defining equations for all geometrically hyperelliptic Shimura curves $X_0(D,N)$. In this paper we compute the $mathbbQ$-rational points on the Atkin-Lehner quotients of these curves using a variety of techniques. We also determine which rational points are CM for many of these curves.

Full work available at URL: https://arxiv.org/abs/2212.04553

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