Singular moduli and the arakelov intersection

The values of the modular y-function at imaginary quadratic arguments in the upper half plane are usually called singular moduli. In this paper, we use the Arakelov intersection to give the prime factorizations of a certain combination of singular moduli, coming from the Hecke correspondence. Such a result may be considered as a degenerate one of Gross and Zagier on Heegner points and derivatives of L-series, and is parellel to the result of Gross and Zagier on singular moduli.