  We consider the problem of counting the number of rational points on the
family of Kummer surfaces associated with two non-isogenous elliptic curves.
For this two-parameter family we prove Manin's unity, using the presentation of
the Kummer surfaces as isotrivial elliptic fibration and as double cover of the
modular elliptic surface of level two. By carrying out the rational point-count
with respect to either of the two elliptic fibrations explicitly, we obtain an
interesting new identity between two-parameter counting functions.
