Weil pairings and Morava K-theory

We give a new proof of a special case of a theorem Hopkins and the authors, relating the Morava K-theory of BU〈6〉 to the theory of cubical structures on formal groups. In the process we relate the Morava K-theory of the Eilenberg-MacLane space K(Z,3) to the theory of Weil pairing, and we appeal to results of algebraic geometers about biextensions.