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