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arXiv · 2212.04553

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

Oana Padurariu·Ciaran Schembri
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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 $\mathbb{Q}$-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.

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Oana Padurariu, Ciaran Schembri. 2022-12-08. Rational points on Atkin-Lehner quotients of geometrically hyperelliptic Shimura curves. https://arxiv.org/abs/2212.04553

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