  It was first pointed out by Weil that we can use classical invariant theory
to compute the Jacobian of a genus one curve. The invariants required for
curves of degree n = 2,3,4 were already known to the nineteenth centuary
invariant theorists. We have succeeded in extending these methods to curves of
degree n = 5, where although the invariants are too large to write down as
explicit polynomials, we have found a practical algorithm for evaluating them.
