\author{J.P.C.Greenlees}
\address{Department of Pure Mathematics, Hicks Building,
Sheffield S3 7RH. UK.}
\author{M.J.Hopkins}
\address{Department of Mathematics, MIT, Cambridge, MA 02139-4307, USA.}
\author{I.Rosu}
\address{Department of Mathematics, MIT, Cambridge, MA 02139-4307, USA.}

Abstract: We give a functorial construction of  a rational 
$S^1$-equivariant cohomology theory from  an elliptic curve equipped 
with suitable coordinate data. The 
elliptic curve may be recovered from the cohomology theory; indeed, 
the  value of the cohomology theory on the compactification of an 
$S^1$-representation is given by the sheaf cohomology of a suitable 
line bundle on the curve. The construction is easy: by considering
functions on the elliptic curve with specified poles one may 
write down the  representing $S^1$-spectrum
in the first author's algebraic model of rational $S^1$-spectra