Integral points of a modular curve of level 11

TL;DR

This paper determines the integral points on a specific modular curve of level 11 using elliptic logarithm bounds, leading to new solutions for class number one problems in quadratic fields.

Contribution

It applies lower bounds for elliptic logarithms to explicitly find integral points on a modular curve of level 11, a novel approach in this context.

Findings

Identified all integral points on the modular curve of level 11.

Derived new solutions to the class number one problem for complex quadratic fields.

Abstract

Using lower bounds for linear forms in elliptic logarithms we determine the integral points of the modular curve associated to the normalizer of a non-split Cartan group of level 11. As an application we obtain a new solution of the class number one problem for complex quadratic fields.