
joint with John Cremona, Catherine O'Neil, Denis Simon and Michael Stoll
This is the second in a series of papers in which we study the nSelmer group of an elliptic curve. In this paper, we show how to realize elements of the nSelmer group explicitly as curves of degree n embedded in P^{n1}. The main tool we use is a comparison between an easily obtained embedding into P^{n21} and another map into P^{n21} that factors through the Segre embedding P^{n1} x P^{n1} > P^{n21}. The comparison relies on an explicit version of the localtoglobal principle for the ntorsion of the Brauer group of the base field.
The other papers in this series are Paper I. Algebra and Paper III. Algorithms.