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Sextic fields containing a quadratic field. I. (Corps sextiques contenant un corps quadratique. I.) (French) Zbl 0719.11087

This is a table containing the first thousand fields (ordered with respect to the size of the absolute value of the discriminant) of algebraic number fields \(K\) of degree six which contain a quadratic subfield and have 6, respectively 4, real conjugates. The following data are listed: the discriminant \(d_ K\) of \(K\), the discriminant \(d_ k\) of the quadratic subfield \(k\), the norm of the relative discriminant \({\mathfrak d}_{K/k}\), the type of the Galois group of the normal closure of \(K\), a generating polynomial \(P(X)\) for \(K/k\), its discriminant \(d_ P\), the discriminant of the quadratic field generated by \(\sqrt{d_ P}\) and the norm of the factor \({\mathfrak f}\) of the decomposition \((d_ P)={\mathfrak f}^ 2{\mathfrak d}_{K/k}\).
The underlying theory appeared in [A.-M. Bergé, J. Martinet and M. Olivier, Math. Comput. 54, 869– 884 (1990; Zbl 0709.11056)].

MSC:

11Y40 Algebraic number theory computations
11R21 Other number fields
11-04 Software, source code, etc. for problems pertaining to number theory
11R29 Class numbers, class groups, discriminants
11R11 Quadratic extensions
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