  The beam energy dependence of $v_4$ (the quadrupole moment of the transverse
radial flow) is sensitive to the nuclear equation of state (EoS) in mid-central
Au + Au collisions at the energy range of $3 < \sqrt{s_{NN}} < 30$ GeV, which
is investigated within the hadronic transport model JAM. Different equations of
state, namely, a free hadron gas, a first-order phase transition and a
crossover 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 positive
contribution to $v_4$ from the squeeze-out of spectator particles which turn
into participants due to the admixture of the strong collective flow in the
shocked, compressed nuclear matter.
