If you are looking for the data and the programs developed for "The minimum discriminant of number fields of degree 8 and signature (2,3)" (older version of the programs) click here

In this page we provide the programs used to classify number fields of degree 8 and degree 9 with low discrminant, for the signatures (2,3), (4,2), (6,1), (1,4) and (3,3). We also present the data collected during the computations.

  • Degree 8, signature (2,3)

  • Degree 8, signature (4,2)

  • Degree 8, signature (6,1)

  • Degree 9, signature (1,4)

  • Degree 9, signature (3,3)

    We finally give tables of number fields with signature (0,4), (8,0) and (9,0) up to certain discriminant bounds.
    The upper bounds are the ones for which is known that the considered fields are the only ones: the references for the choice of the upper bounds and for the fields consist in the following papers. The tables are written in the format used by Megrez for number fields, presenting the discriminant, the coefficients of the minimum polynomial, the class number and the generators of the class group: