We study the focusing 3d cubic NLS equation with H 1 data at the mass-energy threshold, namely, when . In earlier works of Holmer-Roudenko and Duyckaerts-Holmer-Roudenko, the behavior of solutions (i.e., scattering and blow up in finite time) In this paper, we first exhibit 3 special solutions: e it Q and Q ± , where Q is the ground state, Q ± exponentially approach the ground state solution in the positive time direction, Q + has finite time blow up and Q − scatters in the negative time

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... on. Secondly, we classify solutions at this threshold and obtain that up toḢ 1/2 symmetries, they behave exactly as the above three special solutions, or scatter and blow up in both time directions as the solutions below the mass-energy threshold. These results are obtained by studying the spectral properties of the linearized Schrödinger operator in this mass-supercritical case, establishing relevant modulational stability and careful analysis of the exponentially decaying solutions to the linearized equation.