  The goal of the present paper is two-fold. First, we present a classification
of algebraic K3 surfaces polarized by the lattice H+E_8+E_7. Key ingredients
for this classification are: a normal form for these lattice polarized K3
surfaces, a coarse moduli space and an explicit description of the inverse
period map in terms of Siegel modular forms. Second, we give explicit formulas
for a Hodge correspondence that relates these K3 surfaces to principally
polarized abelian surfaces. The Hodge correspondence in question underlies a
geometric two-isogeny of K3 surfaces.
