  In this paper, we develop an algebraic de Rham theory for unipotent
fundamental groups of once punctured elliptic curves over a field of
characteristic zero using the universal elliptic KZB connection of
Calaque-Enriquez-Etingof and Levin-Racinet. We use it to give an explicit
version of Tannaka duality for unipotent connections over an elliptic curve
with a regular singular point at the identity.
