Class groups of quadratic fields. II

Abstract

A computation has been made of the noncyclic class groups of imaginary quadratic fields Q ( − D ) Q(\sqrt { - D} ) for even and odd discriminants − D - D from 0 to − 25000000 - 25000000 . Among the results are that 95% of the class groups are cyclic, and that − 11203620 - 11203620 and − 18397407 - 18397407 are the first discriminants of imaginary quadratic fields for which the class group has rank three in the 5-Sylow subgroup. The latter was known to be of rank three; this computation demonstrates that it is the first odd discriminant of 5-rank three or more.