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From a modern perspective, the class group of a fundamental discriminant ''D'' is [[isomorphic]] to the [[narrow class group]] of the [[quadratic field]] <math>\mathbf{Q}(\sqrt{D})</math> of discriminant ''D''.<ref>{{harvnb|Fröhlich|Taylor|1993|loc=Theorem 58}}</ref> For negative ''D'', the narrow class group is the same as the [[ideal class group]], but for positive ''D'' it may be twice as big.
== Genera of binary quadratic forms ==
Gauss also considered a coarser notion of equivalence, under which the set of binary quadratic forms of a fixed discriminant splits into several genera of forms and each '''[[Genus of a quadratic form|genus]]''' consists of finitely many classes of forms.
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