  We compute the class of arithmetic genus two Teichmueller curves in the
Picard group of pseudo-Hilbert modular surfaces, distinguished according to
their torsion order and spin invariant. As an application, we compute the
number of genus two square-tiled surfaces with these invariants. The main
technical tool is the computation of divisor classes of Hilbert Jacobi forms on
the universal abelian surface over the pseudo-Hilbert modular surface.
