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
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.
