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The Born cross sections of the e+e− → +¯ − and e+e− → −¯ + processes are determined for centerof-mass energy from 2.3864 to 3.0200 GeV with the BESIII detector. The cross section lineshapes can be described properly by a pQCD function and the resulting ratio of effective form factors for the + and − is consistent with 3. In addition, ratios of the + electric and magnetic form factors, |GE /GM |, are obtained at three center-of-mass energies through an analysis of the angular distributions. These measurements, which are studied for the first time in the off-resonance region, provide precision experimental input for understanding baryonic structure. The observed new features of the ± form factors require more theoretical discussions for the hyperons.