Equations for a K3 Lehmer map

Abstract

McMullen proved that there exists an automorphism of minimal topological entropy on a projective K3 surface. We derive equations for the surface and its automorphism. We reconstruct the surface and its automorphism from the Hodge theoretic model provided by McMullen. The approach is computer aided and relies on finite non-symplectic automorphisms, $p$-adic lifting, elliptic fibrations and the Kneser neighbor method for integer lattices.