The magnetohydrodynamic stability of a plasma column with an elliptical cross section to axisymmetric, rigid plasma displacements is analyzed. The considered plasma equilibrium, characterized by the presence of a double-null magnetic separatrix, is found to be unstable. An application of the well-known Energy Principle [I. B. Bernstein, E. A. Frieman, M. D. Kruskal, and R. M. Kulsrud, Proc. R. Soc. London, Ser. A 244, 17 (1958)] is presented, taking into account the effect of external localized electric currents on the mode stability. It is shown that such currents can stabilize the axisymmetric displacements if their values exceed a critical threshold.