Computing integral points on X_ns^+(p)

TL;DR

This paper presents an algorithm to compute integral points on a specific modular curve related to non-split Cartan subgroups, demonstrating that for primes between 7 and 101, the only integral points are CM-points.

Contribution

The paper introduces a new algorithm for computing integral points on modular curves of prime level p associated with non-split Cartan subgroups, confirming the CM-point classification for 7<p<101.

Findings

Only CM-points are integral for 7<p<101

Algorithm effectively computes integral points on the modular curve

Supports classification of integral points on these curves

Abstract

We describe an algorithm for computing integral points on the modular curve of prime level p associated to the normalizer of a non-split Cartan subgroup of GL_2(F_p). Using our method, we show that for 7<p<101 the only integral points on this curve are the CM-points.