  In the studies on the modularity conjecture for rigid Calabi-Yau threefolds
several examples with the unique level 8 cusp form were constructed. According
to the Tate Conjecture correspondences inducing isomorphisms on the middle
cohomologies should exist between these varieties. In the paper we construct
several examples of such correspondences. In the constructions elliptic
fibrations play a crucial role. In fact we show that all but three examples are
in some sense built upon two modular curves from the Beauville list.
