  We describe an algorithm for computing the Picard-Fuchs equation for a family
of twists of a fixed elliptic surface. We then apply this algorithm to obtain
the equation for several examples, which are coming from families of Kummer
surfaces over Shimura curves, as studied in our previous work. We use this to
find correspondenced between the parameter spaces of our families and Shimura
curves. These correspondences can sometimes be proved rigorously.
