The determinant of a binary quadratic form A u^2 + 2B u v + C v^2 is defined as D congruent A C - B^2. It is equal to 1/4 of the corresponding binary quadratic form discriminant. Unfortunately, some authors define the determinant of a binary quadratic form as the negative of D above, so care is needed when consulting the literature.

binary quadratic form | binary quadratic form discriminant | positive definite quadratic form | positive semidefinite quadratic form