  The Gauge/Bethe correspondence relates Omega-deformed N=2 supersymmetric
gauge theories to some quantum integrable models, in simple cases the
integrable models can be treated as solvable quantum mechanics models. For
SU(2) gauge theory with an adjoint matter, or with 4 fundamental matters, the
potential of corresponding quantum model is the elliptic function. If the mass
of matter takes special value then the potential is an elliptic solution of KdV
hierarchy. We show that the deformed prepotential of gauge theory can be
obtained from the average densities of conserved charges of the classical KdV
solution, the UV gauge coupling dependence is assembled into the Eisenstein
series. The gauge theory with adjoint mass is taken as the example.
