We study the physics reach of a low-energy neutrino factory (LENF) and its dependence on the chosen baseline distance, $L$, and stored-muon energy, ${E}_{\ensuremath{\mu}}$, in order to ascertain the configuration of the optimal LENF. In particular, we study the performance of the LENF over a range of baseline distances from 1000 km to 4000 km and stored-muon energies from 4 GeV to 25 GeV, connecting the early studies of the LENF (1300 km, 4.5 GeV) to those of the conventional, high-energy neutrino factory design (4000 km and 7000 km, 25 GeV). Three different magnetized detector options are considered: a Totally-Active Scintillator Detector (TASD) and two models of a liquid-argon detector distinguished by optimistic and conservative performance estimates. In order to compare the sensitivity of each set-up, we compute the full $\ensuremath{\delta}$-dependent discovery contours for the determination of ${\ensuremath{\theta}}_{13}\ensuremath{\ne}0$, ${\ensuremath{\delta}}_{CP}\mathrm{\ensuremath{\in}\ensuremath{\llap{\not\;}}}{0,\ensuremath{\pi}}$ and $\mathrm{sign}(\ensuremath{\Delta}{m}_{13}^{2})$. For large values of ${\ensuremath{\theta}}_{13}$, as recently confirmed by the Daya Bay and RENO experiments, the LENF provides a strong discovery potential over the majority of the $L\mathrm{\text{\ensuremath{-}}}{E}_{\ensuremath{\mu}}$ parameter space and is a promising candidate for the future generation of long baseline experiments aimed at discovering $CP$-violation and the mass hierarchy, and at making a precise determination of the oscillation parameters.