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A Database for Polynomials over the Rationals with WWW Interface

This site contain a database of polynomials up to degree 15 created by Jürgen Klüners and 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 the groups.

Congruence Subgroups of PSL(2,Z) of Genus up to 24

These tables were computed by Chris Cummins and Sebastian Pauli.

Tables of Number Fields with Prescribed Ramification

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.

Database of Local Fields

This site 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.

Denis Simon has a list of polynomials with small discriminant of degree up to 48.

Last modified: 2005-09-28 09:19 (UTC)
The Kant Project