Non-primitive number fields of degree eight and of signature (2,3), (4,2), and (6,1) with small discriminant

Abstract

We give the lists of all non-primitive number fields of degree eight having two, four and six real places of discriminant less than 6688609, 24363884 and 92810082, respectively, in absolute value. For each field in the lists, we give its discriminant, the discriminant of its subfields, a relative polynomial generating the field over one of its subfields and its discriminant, the corresponding polynomial over Q \mathbb {Q} , and the Galois group of its Galois closure.