Many of the groups listed in Chapters 2 and 3 can be described completely without recourse to the composition algorithm. For class numbers 1, 2, and 3, only cyclic groups are possible. For class number 4, only the cyclic or Klein 4-groups are possible, and these can be distinguished by the number of ambiguous forms. Thus, the groups for discriminants −39, −55, −63, −155, −56, −68, and −80 are cyclic, while the groups of discriminants −84 and −96 are not. The structure of these groups then determines the multiplication table completely.
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