  For each elliptic curve A over the rational numbers we construct a 2-periodic
S^1-equivariant cohomology theory E whose cohomology ring is the sheaf
cohomology of A; the homology of the sphere of the representation z^n is the
cohomology of the divisor A(n) of points with order dividing n. The
construction proceeds by using the algebraic models of the author's AMS Memoir
``Rational S^1 equivariant homotopy theory.'' and is natural and explicit in
terms of sheaves of functions on A.
  This is Version 5.2 of a paper of long genesis (this should be the final
version). The following additional topics were first added in the Fourth
Edition:
  (a) periodicity and differentials treated
  (b) dependence on coordinate
  (c) relationship with Grojnowksi's construction and, most importantly,
  (d) equivalence between a derived category of O_A-modules and a derived
category of EA-modules. The Fifth Edition included
  (e) the Hasse square and
  (f) explanation of how to calculate maps of EA-module spectra.
