English

Non-elliptic Shimura curves of genus one

Number Theory 2008-04-25 v2 Algebraic Geometry

Abstract

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.

Keywords

Cite

@article{arxiv.math/0612732,
  title  = {Non-elliptic Shimura curves of genus one},
  author = {Josep Gonzalez and Victor Rotger},
  journal= {arXiv preprint arXiv:math/0612732},
  year   = {2008}
}

Comments

Minor correction in Corollary 5.13 and reference updated