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