  We study a family of hypergeometric motives $H(\alpha,\beta|t)$ attached to a
pair of tuples $\alpha=(1/4,1/2,3/4)$, $\beta=(0,0,0)$. To each such motive we
can attach a system of $\ell$--adic realisations with the trace of geometric
Frobenius given by the evaluation of the finite field analogue of complex
hypergeometric function. Geometry of elliptic fibrations makes it possible to
to realise the motive $H(\alpha,\beta|t)$ as a pure Chow motive attached to a
suitable K3 surface $V_{t}$.
