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A formula for the Jacobian of a genus one curve of arbitrary degree

We extend the formulae of classical invariant theory for the Jacobian of a genus one curve of degree n = 2, 3, 4 to curves of arbitrary degree. To do this, we associate to each genus one normal curve of degree n, an n by 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.


A formula for the Jacobian of a genus one curve of arbitrary degree   (26 pages)     dvi   ps   ps.gz   pdf

A Magma script containing some of the formulae in the paper is available here.