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1998 The $S_5$ extensions of degree 6 with minimum discriminant
David Ford, Michael Pohst, Mario Daberkow, Nasser Haddad
Experiment. Math. 7(2): 121-124 (1998).

Abstract

The algebraic number fields of degree 6 having Galois group $S_5$ and minimum discriminant are determined for signatures (0,\,3), (2,\,2) and (6,\,0). The fields $F_0$, $F_2$, $F_6$ are generated by roots of $f_0(t) = t^6 + 3 t^4 + 2 t^3 + 6 t^2 + 1$, $\,f_2(t) = t^6 - 2 t^4 + 12 t^3 - 16 t + 8$, and $f_6(t) = t^6 - 18 t^4 + 9 t^3 + 90 t^2 - 70 t - 69$ respectively. Each of these fields is unique up to isomorphism. This completes the enumeration of primitive sextic fields with minimum discriminant for all possible combinations of Galois group and signature.

Citation

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David Ford. Michael Pohst. Mario Daberkow. Nasser Haddad. "The $S_5$ extensions of degree 6 with minimum discriminant." Experiment. Math. 7 (2) 121 - 124, 1998.

Information

Published: 1998
First available in Project Euclid: 24 March 2003

zbMATH: 0921.11052
MathSciNet: MR1677099

Subjects:
Primary: 11R21
Secondary: 11R29, 11R32, 11Y40

Rights: Copyright © 1998 A K Peters, Ltd.

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Vol.7 • No. 2 • 1998
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