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The beam energy dependence of $v_4$ (the quadrupole moment of the transverseradial flow) is sensitive to the nuclear equation of state (EoS) in mid-centralAu + Au collisions at the energy range of $3 < \sqrt{s_{NN}} < 30$ GeV, whichis investigated within the hadronic transport model JAM. Different equations ofstate, namely, a free hadron gas, a first-order phase transition and acrossover are compared. An enhancement of $v_4$ at $\sqrt{s_{{NN}}}\approx 6$GeV is predicted for an EoS with a first-order phase transition. This enhanced$v_4$ flow is driven by both the enhancement of $v_2$ as well as the positivecontribution to $v_4$ from the squeeze-out of spectator particles which turninto participants due to the admixture of the strong collective flow in theshocked, compressed nuclear matter.

The enhancement of $v_4$ in nuclear collisions at the highest densities signals a first order phase transition