  In a recent paper Ahlgren, Ono and Penniston described the L-series of K3
surfaces from a certain one parameter family in terms of those of a particular
family of elliptic curves. The Tate conjecture predicts the existence of a
correspondence between these K3 surfaces and certain Kummer surfaces related to
these elliptic curves. A geometric construction of this correspondence is given
here, using results of D. Morrison on Nikulin involutions.
