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In this Letter, a systematic study of the weak radiative hyperon decay Ξ0→Λγ at an electron-positron collider using entangled Ξ0Ξ¯0 pair events is presented. The absolute branching fraction for this decay has been measured for the first time, and is (1.347±0.066stat.±0.054syst.)×10−3. The decay asymmetry parameter, which characterizes the effect of parity violation in the decay, is determined to be −0.741±0.062stat.±0.019syst.. The obtained results are consistent with the world average values within the uncertainties, offering valuable insights into the underlying mechanism governing the weak radiative hyperon decays. The charge conjugation parity (CP) symmetries of branching fraction and decay asymmetry parameter in the decay are also studied. No statistically significant violation of charge conjugation parity symmetry is observed.