Improvements in the computation of ideal class groups of imaginary quadratic number fields

TL;DR

This paper presents enhanced algorithms for computing ideal class groups of imaginary quadratic fields, achieving significant speed-ups and enabling computations with very large discriminants within a week.

Contribution

The paper introduces a large prime strategy and a new linear algebra method, significantly improving the efficiency of class group computations for large discriminants.

Findings

Achieved computation of class groups for discriminants of 110 decimal digits

Implemented a large prime strategy to speed up calculations

Developed a new linear algebra technique for better performance

Abstract

We investigate improvements to the algorithm for the computation of ideal class groups described by Jacobson in the imaginary quadratic case. These improvements rely on the large prime strategy and a new method for performing the linear algebra phase. We achieve a significant speed-up and are able to compute ideal class groups with discriminants of 110 decimal digits in less than a week.