We study tensor powers of rank 1 Drinfeld A-modules, where A is the affine coordinate ring of an elliptic curve. Using the theory of A-motives, we find explicit formulas for the A-action of these modules. Then, by developing the theory of vector valued Anderson generating functions, we give formulas for the coefficients of the logarithm and exponential functions associated to these A-modules, as well as formulas for the fundamental period. This allows us to relate function field zeta values to evaluations of the logarithm function and prove transcendence facts about these zeta values.