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We perform a systematic study of elliptic flow ($v_2$) in Au+Au collision at$\sqrt{s_{NN}}=5$ GeV by using a microscopic transport model JAM. Thecentrality, pseudorapidity, transverse momentum and beam energy dependence of$v_2$ for charged as well as identified hadrons are studied. We investigate theeffects of both the hadronic mean-field and the softening of equation of state(EoS) on elliptic flow. The softening of EoS is realized by imposing attractiveorbits in two body scattering, which can reduce the pressure of the system. Wefound that the softening of EoS leads to the enhancement of $v_2$, while thehadronic mean-field suppresses $v_2$ relative to the cascade mode. It indicatesthat elliptic flow at high baryon density regions is highly sensitive to theEoS and the enhancement of $v_2$ may probe the signature of a first-order phasetransition in heavy-ion collisions at beam energies of a strong baryon stoppingregion.

Effects of mean-field and the softening of equation of state on elliptic flow in Au+Au collision at $\sqrt{s_{NN}}$ = 5 GeV from JAM model