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1992 The totally real {$A\sb 5$} extension of degree {$6$} with minimum discriminant
David Ford, Michael Pohst
Experiment. Math. 1(3): 231-235 (1992).

Abstract

We determine the totally real algebraic number field $F$ of degree 6 with Galois group $A_5$ and minimum discriminant, showing that it is unique up to isomorphism and that it is generated by a root of the polynomial $$ f(t) = t^6 - 10 t^4 + 7 t^3 + 15 t^2 - 14 t + 3 $$ over the rationals. We also list the fundamental units and class number of $F$, as well as data for several other fields that arose in our computations and that might be of interest.

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David Ford. Michael Pohst. "The totally real {$A\sb 5$} extension of degree {$6$} with minimum discriminant." Experiment. Math. 1 (3) 231 - 235, 1992.

Information

Published: 1992
First available in Project Euclid: 25 March 2003

zbMATH: 0773.11067
MathSciNet: MR1203877

Subjects:
Primary: 11R80
Secondary: 11R29 , 11Y40

Rights: Copyright © 1992 A K Peters, Ltd.

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Vol.1 • No. 3 • 1992
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