Computation of a cover of Shimura curves using a Hurwitz space

International audienceUsing a Hurwitz space computation, we determine the canonical model of the cover of Shimura curves $X_0(2) \to X(1)$ associated to the quaternion algebra over the cubic field of discriminant~$13^2$, which is ramified at exactly two real places and unramified at finite places. Then, we list the coordinates of some rational CM points on~$X(1)$