English

Rational points on Atkin-Lehner quotients of geometrically hyperelliptic Shimura curves

Number Theory 2022-12-12 v1

Abstract

Guo and Yang give defining equations for all geometrically hyperelliptic Shimura curves X0(D,N)X_0(D,N). In this paper we compute the Q\mathbb{Q}-rational points on the Atkin-Lehner quotients of these curves using a variety of techniques. We also determine which rational points are CM for many of these curves.

Keywords

Cite

@article{arxiv.2212.04553,
  title  = {Rational points on Atkin-Lehner quotients of geometrically hyperelliptic Shimura curves},
  author = {Oana Padurariu and Ciaran Schembri},
  journal= {arXiv preprint arXiv:2212.04553},
  year   = {2022}
}

Comments

23 pages. Comments welcome!