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Abstract
The algebraic number fields of degree 6 having Galois group S5 and minimum discriminant are determined for signatures (0, 3), (2,2) and (6,0). The fields F0, F2, F6 are generated by roots of f0(t) = t6 3t4 + 2t3 + 6t2 + 1, f2(t) = t6 – 2t4 + 12t3 – 16t + 8, and f6(t) = t6 – 18t4 + 9t3 + 90t2 – 70t – 69 respectively. Each of these fields is unique up to isomorphism. This completes the enumeration of primitive sextic fields with min imum discriminant for all. possible combinations of Galois group and signature.