Computation of a cover of Shimura curves using a Hurwitz space

Emmanuel Hallouin (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

Using 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~$X(1)$.

Domaines: Théorie des nombres [math.NT]

Emmanuel Hallouin. Computation of a cover of Shimura curves using a Hurwitz space. Journal of Algebra, 2009, 351 (2), pp.558-566. ⟨hal-00975438⟩