We let denote the classical modular group, ie. the group of matrices with integer coefficients with determinant +1. The elements of act on a given binary quadratic form in a natural way. Consider the form

The matrix

acts on f as follows. Under the transformation

the form f is transformed into the form


and has discriminant

This defines an equivalence relation . Also note that the discriminant is invariant. The number of equivalence classes of forms of a given discriminant , is called the class number . Below is table of class numbers for forms with negative discriminant.