  We extend the formulae of classical invariant theory for the Jacobian of a
genus one curve of degree $n \le 4$ to curves of arbitrary degree. To do this,
we associate to each genus one normal curve of degree $n$, an $n \times n$
alternating matrix of quadratic forms in $n$ variables, that represents the
invariant differential. We then exhibit the invariants we need as homogeneous
polynomials of degrees $4$ and $6$ in the coefficients of the entries of this
matrix.
