  We prove that certain differential operators of the form $DLD$ with $L$
hypergeometric and $D=z \frac{d}{dz}$ are of Picard-Fuchs type. We give closed
hypergeometric expressions for minors of the biextension period matrices that
arise from certain rank 4 weight 3 Calabi-Yau motives presumed to be of
analytic rank 1. We compare their values numerically to the first derivative of
the $L$-functions of the respective motives at $s=2$.
