Corps sextiques contenant un corps cubique. III. (Sextic fields with a cubic field. III). (French) Zbl 0726.11081

Olivier, Michel

Sémin. Théor. Nombres Bordx., Sér. II 3, No. 1, 201-245 (1991).

[Parts I, II cf. Sémin. Théor. Nombres Bordx., Sér. II 1, 205-250 (1989; Zbl 0719.11087) and ibid. Ser. II 2, 49-102 (1990; Zbl 0719.11088).]
These are tables of sixth degree algebraic number fields K containing a cubic but no quadratic subfield. For each possibility for the number of real conjugates of K and for the subfield being totally real or not (a total of six cases) the first 200 fields with respect to the size of the absolute value of the discriminant are presented with the following data:
the absolute value \(d_ K\) of the discriminant of K, the discriminant \(d_{K_ 0}\) of the cubic subfield, the norm of the relative discriminant \({\mathfrak d}_{K/K_ 0}\), the type of the Galois group of the normal closure of K, a generating polynomial P(X) for \(K/K_ 0\), its discriminant \(d_ P\), and the norm of the factor \({\mathfrak f}\) of the decomposition \((d_ P)={\mathfrak f}^ 2{\mathfrak d}_{K/K_ 0}.\)
The underlying theory is to appear in “Sextic fields with a cubic subfield and no quadratic subfield”, Math. Comput. (1992).

Reviewer: M.Pohst (Düsseldorf)

MSC:

11Y40	Algebraic number theory computations
11R29	Class numbers, class groups, discriminants
11R21	Other number fields
11-04	Software, source code, etc. for problems pertaining to number theory
11Y16	Number-theoretic algorithms; complexity

Keywords:

table of sextic fields; tables; discriminant; Galois group of the normal closure; generating polynomial

Citations:

Zbl 0719.11087; Zbl 0719.11088