  We present a method to calculate the action of the Mordell-Weil group of an
elliptic K3 surface on the numerical N\'eron-Severi lattice of the K3 surface.
As an application, we compute a finite generating set of the automorphism group
of a K3 surface birational to the double plane branched along a 6-cuspidal
sextic curve of torus type.
