  Bruinier and Yang conjectured a formula for an intersection number on the
arithmetic Hilbert modular surface, CM(K).T_m, where CM(K) is the zero-cycle of
points corresponding to abelian surfaces with CM by a primitive quartic CM
field K, and T_m is the Hirzebruch-Zagier divisors parameterizing products of
elliptic curves with an m-isogeny between them. In this paper, we examine
fields not covered by Yang's proof of the conjecture. We give numerical
evidence to support the conjecture and point to some interesting anomalies. We
compare the conjecture to both the denominators of Igusa class polynomials and
the number of solutions to the embedding problem stated by Goren and Lauter.
