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We compute the canonical model of the cover of Shimura curves $X_0(2) \toX(1)$ for the cubic field of discriminant 13^2 described at the end of Elkies'paper "Shimura curves for level 3 subgroups of the (2,3,7) triangle group".Last, we list the coordinates of some rational CM points on X(1).

Computation of the cover of Shimura curves $X_0(2) \to X(1)$ for the cyclic cubic field of discriminant 13^2