Minimum Discriminants of Imprimitive Decic Fields

Abstract

In this paper, we compute the minimum discriminants of imprimitive degree-10 fields for different combinations of Galois group and signature. We use class field theory when there is a quintic subfield, and a Martinet search in the more difficult case in which there is only a quadratic subfield.

A database of number fields

“…In a few cases, we obtained polynomials from other sources, notably for number fields of small discriminant: those compiled by the Bordeaux group [7], which in turn were computed by several authors, and the tables of totally real fields of Voight [39,40]. In addition, we include fields found by the authors in joint work with others [13,24].…”