Abstract: Order configuration spaces on an elliptic curve (topologically a 2-torus) are small non-trivial examples of configuration spaces on closed varieties. However, their cohomology is not well-understood: it can be described using the Kriz model, but its Betti numbers are unknown. We will apply recent techniques of representation theory in order to simplify the Kriz model of elliptic curves and obtain information about Betti numbers and their growth.