Shioda described a method to compute the Lefschetz number of a Delsarte surface. In one of his examples he uses this method to compute the rank of an elliptic curve over k(t). In this article we find all elliptic curves over k(t) for which his method is applicable. For these curves we also compute the maximal Mordell-Weil rank.
['Bas Heijne']
The maximal rank of elliptic Delsarte surfaces