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
where
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.