Quadratic fields with 3-rank equal to 4

In [21 there is reference to 119 known imaginary quadratic fields that have 3-rank r > 4. We examine these fields and determine the exact values of r. Their associated real filelds and the distribution of their 3-Sylow subgroups are also studied. Some of the class groups are recorded since they are of special interest. These include examples having an infinite class field tower and only one ramified prime, and others having an infinite tower because of two different components of