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We prove that certain differential operators of the form 
$ DLD $ with 
$ L $ hypergeometric and 
$ D=z\frac{\partial }{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 $.
