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The totally real \(A_ 5\) extension of degree 6 with minimum discriminant. (English) Zbl 0773.11067

The title refers to the equation \(f(t)=t^ 6-10t^ 4+7t^ 3+15t^ 2- 14t+3\). The discriminant \((d=5567^ 2)\) and the class number (one) are also given together with the units. The techniques are sensitive to signature and Galois group [see M. Pohst, Math. Comput. 48, 309-314 (1987; Zbl 0632.12001)]. Related results are summarized.
Reviewer: H.Cohn (New York)

MSC:

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

Citations:

Zbl 0632.12001
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References:

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