I give the results of a detailed reanalysis of the 13 TeV TOTEM
measurement of the differential elastic cross section at very low
momentum transfer. We obtain estimates similar to thos of TOTEM
for the rho parameter, but a significantly lower total cross section.
I then discuss whether these results imply the existence of an
charge-parity-odd exchange, the odderon, at t=0. This seminar is
based on arXiv:1901.05863 .