  Haile, Han and Kuo have studied certain non-commutative algebras associated
to a binary quartic or ternary cubic form. We extend their construction to
pairs of quadratic forms in four variables, and conjecture a further
generalisation to genus one curves of arbitrary degree. These constructions
give an explicit realisation of an isomorphism relating the Weil-Chatelet and
Brauer groups of an elliptic curve.
