We have studied the vector to pseudoscalar conversion decay phi -> eta e+e-, with eta -> pi0pi0pi0, with the KLOE detector at DAPHNE. The data set of 1.7 fb-1 of e+e- collisions at sqrt(s)~Mphi contains a clear conversion decay signal of ~31,000 events from which we measured a value of BR(phi -> eta e+e-)=(1.075+-0.007+-0.038)x10-4. The same sample is used to determine the transition form factor by a fit to the e+e- invariant mass spectrum, obtaining b(phi eta) =(1.17 +- 0.10 + 0.07) GeV-2, that improves by a factor of five the precision of the previous measurement and is in good agreement with VMD expectations.
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