The transverse-momentum integrated elliptic flow of charged particles at midrapidity, v2(charged), and that of identified hadrons from Au+Au collisions are computed in a wide range of incident energies 2.7 GeV ≤ √ sNN ≤ 39 GeV. The simulations are performed within a three-fluid model employing three different equations of state (EoS's): a purely hadronic EoS and two versions of the EoS involving the deconfinement transition-a first-order phase transition and a smooth crossover one. The present simulations demonstrate low sensitivity of v2(charged) to the EoS. All considered scenarios equally well reproduce recent STAR data on v2(charged) for mid-central Au+Au collisions and properly describe its change of sign at the incident energy decrease below √ sNN ≈ 3.5 GeV.The predicted integrated elliptic flow of various species exhibits a stronger dependence on the EoS. A noticeable sensitivity to the EoS is found for anti-baryons and, to a lesser extent, for K − mesons. In particular, the v2 excitation functions of anti-baryons exhibit a non-monotonicity within the deconfinement scenarios that was predicted by Kolb, Sollfrank and Heinz. However, low multiplicities of anti-baryons at √ sNN ≤ 10 GeV result in large fluctuations of their v2 which may wash out this non-monotonicity.