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 $< {10^6}$ 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 ${T_2}$ criterion of Pohst was applied to reduce the number of redundant examples.