To study the nature of the state Y (2175), a dedicated data set of e+e− collision data was collected at the center-of-mass energy of 2.125 GeV with the BESIII detector at the BEPCII collider. By analyzing large-angle Bhabha scattering events, the integrated luminosity of this data set is determined to be 108.49±0.02±0.85 pb−1, where the first uncertainty is statistical and the second one is systematic. In addition, the center-of-mass energy of the data set is determined with radiative dimuon events to be 2126.55±0.03±0.85 MeV, where the first uncertainty is statistical and the second one is systematic.