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Guo and Yang give defining equations for all geometrically hyperellipticShimura curves $X_0(D,N)$. In this paper we compute the $\mathbb{Q}$-rationalpoints on the Atkin-Lehner quotients of these curves using a variety oftechniques. We also determine which rational points are CM for many of thesecurves.

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