Hypergeometric motive (awaiting review)

Hypergeometric motives $H(A,B,t)$ in a family $H(A,B)$ are indexed by rational numbers $t \not \in \{0,1\}$, with the case $t=1$ allowed if special attention is given.

For example $H([3],[1,1],t)$ is the motive $H^1(E_{1728t},{\Bbb Q})$ where $E_{j}$ is an elliptic curve with $j$-invariant $1728j$. Also special hypergeometric motives $H(A,B,1)$ are defined, having degree $1$ or $2$ less than the other $H(A,B,t)$.