Imaginary Multiquadratic Fields of Class Number Dividing $2^m$

TL;DR

This paper presents an algorithm to identify all imaginary multiquadratic fields with class number dividing powers of two, utilizing known lists of quadratic fields, and provides a complete classification for class number dividing 32.

Contribution

It introduces a method to find all such fields based on existing quadratic field data and establishes bounds on their degrees.

Findings

Developed an algorithm for classifying imaginary multiquadratic fields with specific class number bounds.

Provided a complete list of imaginary multiquadratic fields with class number dividing 32.

Established bounds on the degree of these fields.

Abstract

This paper gives a method to find all imaginary multiquadratic fields of class number dividing $2^{m},$ provided the list of all imaginary quadratic fields of class number dividing $2^{m+1}$ is known. We give a bound on the degree of such fields. As an application of this algorithm, we compute a complete list of imaginary multiquadratic fields with class number dividing $32.$