The KANT Group:
[Institut für Mathematik,
contain a database of polynomials up to degree 15 created
Gunter Malle. It 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
the minimal fields in degree 8 for all imprimitive groups and
some of the primitive cases are included.
The aim of the database is to cover all
These tables were computed by Chris Cummins and
This site by John Jones contains tables of number fields of low degree which are
ramified at only a
few small primes. Except where an entry is listed as "preliminary",
the tables are believed to be exhaustive. Check back since the number of tables will
expand over time.
by John W. Jones and David P. Roberts
contains complete tables of low degree extensions of
Qp, for small p. You can
enter a polynomial and find the factors of p-adic
algebra it defines in terms of entries from the tables, and
bound the Galois root discriminant of a global field.
Fields and Polynomials with Small Discriminant
The Bordeaux ftp site
has tables of number fields up to degree 7.
The emphasis there are on fields with small absolute discriminant.
list of polynomials with small discriminant of degree up to 48.
Last modified: 2005-09-28 09:19 (UTC)
The Kant Project