# A Database for Number Fields

## Introduction

This site contains a database of number fields up to degree 19 created by

Jürgen Klüners and

Gunter Malle.
The number fields are represented by a minimal polynomial of a primitive element.
The database contains polynomials for all transitive groups up to that degree, even for most of the possible combinations of signature and Galois group.
Up to degree 7 the fields with minimal (absolute) discriminant with given Galois group and signature have been included.
Furthermore we have included the minimal fields in degree 8 for all imprimitive groups and some of the primitive cases.
Most of these minima were known before our work started.
In our

paper we give a large bibliography of works related to this problem.
The aim of our database is to cover all the groups.
Therefore we only have relatively few polynomials in degree 2, for example.
Check other databases for huge tables in small degree.

The following pages give some overview about the contents of the database.
For every group we give the number of polynomials for each signature contained in the database.
Furthermore we give the minimal field discriminant (known to us) for each entry.

Comments and references for the minima
Links to other databases## Group database - Choose a group degree

Groups are ordered by their degree. Click on one of the boxes below to choose the displayed degree.