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The beam energy dependence of the elliptic flow,$v_2$, is studied inmid-central Au+Au collisions in the energy range of $3\leq \sqrt{s_{NN}} \leq30$ GeV within the microscopic transport model JAM. The results of threedifferent modes of JAM are compared; cascade-,hadronic mean field-, and a newmode with modified equations of state, with a first order phase transition(1.O.P.T.) and with a crossover transition. The standard hadronic mean fieldsuppresses $v_2$, while the inclusion of the effects of a 1.O.P.T. (and also ofa crossover transition) does enhance $v_2$ at $\sqrt{s_{NN}}<30$ GeV. Theenhancement or suppression of the scaled energy flow, dubbed "elliptic flow"isunderstood as being due to out of plane- flow, i.e. $v_2<0$, dubbed out ofplane - "squeeze-out", which occurs predominantly in the early, compressionstage. Subsequently, the in-plane flow dominates, in the expansion stage, $v_2> 0$. The directed flow, dubbed "bounce- off", is an independent measure of thepressure, which quickly builds up the transverse momentum transfer in thereaction plane. When the spectator matter leaves the participant fireballregion, where the highest compression occurs, a hard expansion leads to larger$v_2$. A combined analysis of the three transverse flow coefficients, radial$v_0$-, directed $v_1$- and elliptic $v_2$- flow, in the beam energy range of$3\leq\sqrt{s_{NN}}\leq10$ GeV, distinguishes the different compression andexpansion scenarios: a characteristic dependence on the early stage equation ofstate is observed. The enhancement of both the elliptic and the transverseradial flow and the simultaneous collapse of the directed flow of nucleonsoffers a clear signature if 1.O.P.T. is realized at the highest baryondensities created in high energy heavy-ion collisions.

Enhancement of elliptic flow can signal a first order phase transition in high energy heavy ion collisions