Computation of a cover of Shimura curves using a Hurwitz space

Using a Hurwitz space computation, we determine the canonical model of the cover of Shimura curves X0(2)→X(1) associated to the quaternion algebra over the cubic field of discriminant 132, which is ramified at exactly two real places and unramified at finite places. Then, we list the coordinates of some rational CM points on X(1).