The Totally Real A_{6} Extension of Degree 6 with Minimum Discriminant

David Ford Michael Pohst

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} + 21t^{2} + 9t + 1 over the rationals. We also give an integral basis and list the fundamental units and class number of F.