Supersingular K3 Surfaces in Characteristic 2 as Double Covers of a Projective Plane

For every supersingular K3 surface X in characteristic 2, there exists a homogeneous polynomial G of degree 6 such that X is birational to the purely inseparable double cover of P defined by w = G. We present an algorithm to calculate from G a set of generators of the numerical Néron-Severi lattice of X. As an application, we investigate the stratification defined by the Artin invariant on a moduli space of supersingular K3 surfaces of degree 2 in characteristic 2.