Geometry and Arithmetic of Certain Double Octic Calabi–Yau Manifolds

We study Calabi–Yau manifolds constructed as double coverings of ℙ 3 branched along an octic surface. We give a list of 87 examples corresponding to arrangements of eight planes defined over ℚ. The Hodge numbers are computed for all examples. There are 10 rigid Calabi–Yau manifolds and 14 families with h 1,2 = 1. The modularity conjecture is verified for all the rigid examples.