## 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

### Citations:

Zbl 0719.11088; Zbl 0709.11056
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