We present explicit models for non-elliptic genus one Shimura curves with -level structure arising from an indefinite quaternion algebra of reduced discriminant , and Atkin-Lehner quotients of them. In addition, we discuss and extend Jordan's work [10, Ch. III] on points with complex multiplication on Shimura curves.
Josep GONZÁLEZ. Victor ROTGER. "Non-elliptic Shimura curves of genus one." J. Math. Soc. Japan 58 (4) 927 - 948, October, 2006. https://doi.org/10.2969/jmsj/1179759530