  The combinatorial type of an elliptic K3 surface with a zero section is the
pair of the ADE -type of singular fibers and the torsion part of the
Mordell-Weil group. We determine the set of connected components of the moduli
of elliptic K3 surfaces with fixed combinatorial type. Our method relies on the
theory of Miranda and Morrison on the structure of a genus of even indefinite
lattices, and computer-aided calculations of p-adic quadratic forms.
