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

Guo and Yang give defining equations for all geometrically hyperelliptic Shimura curves \(X_0(D,N)\). In this paper we compute the \(\mathbb{Q}\)-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 th...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2022-12
Main Authors: Padurariu, Oana, Schembri, Ciaran
Format: Article
Language:English
Subjects:
Quotients
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Guo and Yang give defining equations for all geometrically hyperelliptic Shimura curves \(X_0(D,N)\). In this paper we compute the \(\mathbb{Q}\)-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.
ISSN:2331-8422