There are generally finitely many equivalence classes of representations of an integer "n" by forms of given nonzero discriminant formula_28. A complete set of representatives for these classes can be given in terms of "reduced forms" defined in the section below. When formula_29, every representation is equivalent to a unique representation by a reduced form, so a complete set of representatives is given by the finitely many representations of "n" by reduced forms of discriminant formula_28. When formula_117, Zagier proved that every representation of a positive integer "n" by a form of discriminant formula_28 is equivalent to a unique representation formula_119 in which "f" is reduced in Zagier's sense and formula_120, formula_121. The set of all such representations constitutes a complete set of representatives for equivalence classes of representations.