c=2 rational toroidal conformal field theories via the gauss product

We find a concise relation between the moduli tau, rho of a rational Narain lattice Gamma(tau, rho) and the corresponding momentum lattices of left and right chiral algebras via the Gauss product. As a byproduct, we find an identity which counts the cardinality of a certain double coset space defined for isometrics between the discriminant forms of rank two lattices.