The integrated elliptic flow of charged particles produced in Pb+Pb collisions at root S-NN = 2.76 TeV has been measured with the ATLAS detector using data collected at the Large Hadron Collider. The anisotropy parameter, upsilon(2), was measured in the pseudorapidity range |eta| <= 2.5 with the event-plane method. In order to include tracks with very low transverse momentum p(T), thus reducing the uncertainty in upsilon(2) integrated over p(T), a 1 mu b(-1) data sample recorded without a magnetic field in the tracking detectors is used. The centrality dependence of the integrated upsilon(2) is compared to other measurements obtained with higher PT thresholds. The integrated elliptic flow is weakly decreasing with |eta|. The integrated upsilon 2 transformed to the rest frame of one of the colliding nuclei is compared to the lower-energy RHIC data.