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Explicit upper bounds are developed for the class number and the regulator of any cubic field with a negative discriminant. Lower bounds on the class number are also developed for certain special pure cubic fields.

Abstract.Two different computational techniques for determining the class number of a pure cubic field are discussed. These techniques were implemented on an IBM/370-158 computer, and the class number for each pure cubic field Q(D ' ) for D = 2, 3.9999 was obtained. Several tables are presented which summarize the results of these computations. Some theorems concerning the class group structure of pure cubic fields are also given. The paper closes with some conjectures which were inspired by the computer results.