Modular Invariance and the Odderon

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.