Class groups of imaginary biquadratic fields

TL;DR

This paper constructs two infinite families of imaginary biquadratic fields with large class groups, utilizing elliptic and hyperelliptic curves, and builds on prior results from Soleng and Banerjee-Hoque.

Contribution

It introduces two new infinite families of imaginary biquadratic fields with large class groups using novel curve-based constructions.

Findings

Two infinite families of imaginary biquadratic fields with large class groups.

Construction methods involve elliptic and hyperelliptic curves.

Utilizes key results from Soleng and Banerjee-Hoque.

Abstract

We present two distinct families of imaginary biquadratic fields, each of which contains infinitely many members, with each member having large class groups. Construction of the first family involves elliptic curves and their quadratic twists, whereas to find the other family, we use a combination of elliptic and hyperelliptic curves. Two main results are used, one from Soleng and the other from Banerjee and Hoque.