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Proceedings of the London Mathematical Society Advance Access published online on April 25, 2008
Proceedings of the London Mathematical Society, doi:10.1112/plms/pdn021
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© 2008 London Mathematical Society

The invariants of a genus one curve

Tom Fisher

Department of Pure Mathematics and Mathematical Statistics
Centre for Mathematical Sciences
University of Cambridge
Wilberforce Road
Cambridge
CB3 0WB
United Kingdom

Received 29 May 2007. Revision received 4 March 2008.

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 century 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.

2000 Mathematics Subject Classification 11G05, 11Y40, 13A50, 14H25.


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