The Totally Real A6 Extension of Degree 6 with Minimum Discriminant

Abstract

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 — 24t ⁴ + 2lt ² + 9t + 1 over the rationals. We also give an integral basis and list the fundamental units and class number of F.