Context. Globular clusters are known to host multiple stellar populations, which are a signature of their formation process. The globular cluster E3 is one of the few low-mass globulars that is thought not to host multiple populations. Aims. We investigate red giant branch stars in E3 with the aim of providing a first detailed chemical inventory for this cluster, we determine its radial velocity, and we provide additional insights into the possible presence of multiple populations in this cluster. Methods. We obtained high-resolution FLAMES-UVES/VLT spectra of four red giant branch stars likely members of E3. We performed a local thermodynamic equilibrium abundance analysis based on one-dimensional plane parallel ATLAS9 model atmospheres. Abundances were derived from line equivalent widths or spectrum synthesis. Results. We measured abundances of Na and of iron peak (Fe, V, Cr, Ni, Mn), α(Mg, Si, Ca, Ti), and neutron capture elements (Y, Ba, Eu). The mean cluster heliocentric radial velocity, metallicity, and sodium abundance ratio are ν_helio = 12.6 ± 0.4 km s⁻¹(σ = 0.6 ± 0.2 km s⁻¹), [Fe/H] = −0.89 ± 0.08 dex, and [Na/Fe] = 0.18 ± 0.07 dex, respectively. The low Na abundance with no appreciable spread is suggestive of a cluster dominated by first-generation stars in agreement with results based on lower resolution spectroscopy. The low number of stars observed does not allow us to rule out a minor population of second-generation stars. The observed chemical abundances are compatible with the trends observed in Milky Way stars.