Fields with Small GRD

Guide to these tables

Below are are tables of fields with small Galois Root Discriminant (GRD). They are sorted by Galois group, with an emphasis on non-abelian groups. Files can be downloaded as gp files of polynomials, or printable pdf, which has other data included.

The number of distinct Galois fields is given. In some cases, polynomials for non-isomorphic fields with isomorphic Galois closures are listed. Groups only appear for their lowest degree permutation representation. In some cases, tables will contain polynomials of higher degree which have the same Galois closure.

Status flags are either C meaning that the table is proven complete by an exhaustive computation; L for likely to be complete, but not proven; <B for some bound B to indicate that they are proven complete up that the given bound. A blank status flag indicates that we have no information about the completeness of the corresponding table.

Credits

Rachel Wallington has certified the completeness of the entries for 6T10 and 6T13, and contributed new complete entries for 7T2, 7T3, 7T4, solvable octics, and 12T5.

The SL₂(16) field comes from a paper by Johan Bosman.