## The totally real $$A_ 6$$ extension of degree 6 with minimum discriminant.(English)Zbl 0799.11052

Summary: The totally real algebraic number field $$F$$ of degree 6 with Galois group $$A_ 6$$ and minimum discriminant is determined. It is unique up to isomorphy and is generated by a root of the polynomial $$t^ 6- 24 t^ 4+ 21t^ 2+ 9t +1$$ over the rationals. The authors also give an integral basis and list the fundamental units and class number of $$F$$.
In [ibid. 1, 231-235 (1992; Zbl 0773.11067)] the authors gave details of a computation to determine the (unique) totally real algebraic number field of degree 6 having Galois group $$A_ 5$$ and minimum discriminant. There they indicated how the same computation could be extended to give the totally real sextic field with Galois group $$A_ 6$$ of minimum discriminant. This computation has now been completed.

### MSC:

 11R29 Class numbers, class groups, discriminants 11R21 Other number fields 11R80 Totally real fields 11Y40 Algebraic number theory computations

Zbl 0773.11067
Full Text:

### References:

 [1] Ford D., Experimental Math. 1 pp 231– (1992) · Zbl 0773.11067
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