The computation of sextic fields with a cubic subfield and no quadratic subfield

Abstract

We describe six tables of sixth-degree fields K containing a cubic subfield k and no quadratic subfield: one for totally real sextic fields, one for sextic fields with four real places, two for sextic fields with two real places, and two for totally imaginary sextic fields (depending on whether the cubic subfield is totally real or not). The tables provide for each possible discriminant d K {d_K} of K a quadratic polynomial which defines K/k , the discriminant of the cubic subfield and the Galois group of a Galois closure N / Q N/\mathbb {Q} of K / Q K/\mathbb {Q} .