The invariants of a genus one curve

Abstract. It was first pointed out by Weil [26] 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. 1