2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/159716We present explicit models for non-elliptic genus one Shimura curves X_0(D, N) with Gamma_0(N)-level structure arising from an indefinite quaternion algebra of reduced discriminant D, and Atkin-Lehner quotients of them. In addition, we discuss and extend Jordan's work in his Ph. D Thesis on points with complex multiplication on Shimura curves.Minor correction in Corollary 5.13 and reference updatedNumber TheoryAlgebraic Geometry11G18, 14G35text