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Explicit n-descent on elliptic curves, I. Algebra

joint with John Cremona, Catherine O'Neil, Denis Simon and Michael Stoll

This is the first in a series of papers in which we study the n-Selmer group of an elliptic curve, with the aim of representing its elements as genus one normal curves of degree n. The methods we describe are practical in the case n = 3 for elliptic curves over the rationals, and have been implemented in Magma.

Explicit n-descent on elliptic curves, I. Algebra   (37 pages)     dvi   ps   ps.gz   pdf

The other papers in this series are Paper II. Geometry and Paper III. Algorithms.