In this talk we present some links of the theory of the odderon with e
lliptic curves. These results were obtained in an earlier work [19]. T
he natural degrees of freedom of the odderon turn out to coincide with
conformal invariants of elliptic curves with a fixed 'sign'. This lea
ds to a formulation of the odderon which is modular invariant with res
pect to Gamma(2) - the unique normal subgroup of SL(2, Z) of index 2.