  We identify a new symmetry for the equations governing odderon amplitudes,
corresponding in the Regge limit of QCD to the exchange of 3 reggeized gluons.
The symmetry is a modular invariance with respect to the unique normal subgroup
of sl(2,Z) {\,} of index 2.
  This leads to a natural description of the Hamiltonian and conservation-law
operators as acting on the moduli space of elliptic curves with a fixed
``sign'': elliptic curves are identified if they can be transformed into each
other by an {\em even} number of Dehn twists.
