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A genus one curve C of degree 5 is defined by the 4 × 4 Pfaffians of a 5 × 5 alternating matrix of linear forms on P⁴. We prove a result characterising the covariants for these models in terms of their restrictions to the family of curves parametrised by X(5). We then construct covariants describing the covering map of degree 25 from C to its Jacobian and give a practical algorithm for evaluating them.

Invariant theory for the elliptic normal quintic, II. The covering map   (22 pages)          

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