The Picard-Fuchs equation of a family of Calabi-Yau threefolds without maximal unipotent monodromy

Recently, J.C. Rohde constructed families of Calabi–Yau threefolds parametrized by Shimura varieties. The points corresponding to threefolds with complex multiplication are dense in the Shimura variety, and moreover, the families do not have boundary points with maximal unipotent monodromy. Both aspects are of interest for mirror symmetry. In this paper we discuss one of Rohde’s examples in detail, and we explicitly give the Picard–Fuchs equation for this one-dimensional family.