Enumeration of quartic fields of small discriminant

Abstract

With the mixed-type case now completed, all algebraic number fields of degree 4 with absolute discriminant > 10 6 > {10^6} have been enumerated. Methods from the totally real and totally complex cases were used without major modification. Isomorphism of fields was determined by a method similar to one of Lenstra. The T 2 {T_2} criterion of Pohst was applied to reduce the number of redundant examples.