Non-elliptic Shimura curves of genus one

Mathematics – Number Theory

Scientific paper

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Minor correction in Corollary 5.13 and reference updated

Scientific paper

We 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.

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