The integrated elliptic flow of charged particles produced in Pb+Pb collisions at [Formula: see text] TeV has been measured with the ATLAS detector using data collected at the Large Hadron Collider. The anisotropy parameter, [Formula: see text], was measured in the pseudorapidity range [Formula: see text] with the event-plane method. In order to include tracks with very low transverse momentum [Formula: see text], thus reducing the uncertainty in [Formula: see text] integrated over [Formula: see text], a [Formula: see text] data sample recorded without a magnetic field in the tracking detectors is used. The centrality dependence of the integrated [Formula: see text] is compared to other measurements obtained with higher [Formula: see text] thresholds. The integrated elliptic flow is weakly decreasing with [Formula: see text]. The integrated [Formula: see text] transformed to the rest frame of one of the colliding nuclei is compared to the lower-energy RHIC data.