Mixed Degree Number Field Computations

We present a method for computing complete lists of number fields in cases where the Galois group, as an abstract group, appears as a Galois group in smaller degree. We apply this method to find the 25 octic fields with Galois group PSL₂(7) and smallest absolute discriminant. We carry out a number of related computations, including determining the octic field with Galois group 2³:GL₃(2) of smallest absolute discriminant

A database of number fields

We describe an online database of number fields which accompanies this paper. The database centers on complete lists of number fields with prescribed invariants. Our description here focuses on summarizing tables and connections to theoretical issues of current interest.This is the authors' final manuscript as accepted. The final published version can be viewed at LMS JOURNAL OF COMPUTATION AND MATHEMATICS, 17(1), 595-618. Copyright Cambridge University Press 2014 DOI: http://dx.doi.org/10.1112/S146115701400042