  The lowest neutron star masses currently measured are in the range
$1.0-1.1~M_\odot$, but these measurement have either large uncertainties or
refer to isolated neutron stars. The recent claim of a precisely measured mass
$M/M_{\odot} = 1.174 \pm 0.004$ by Martinez et al [Astrophys. J. 812, 143
(2015)] in a double neutron star system suggests that low-mass neutron stars
may be an interesting target for gravitational-wave detectors. Furthermore,
Sotani et al [PTEP 2014, 051E01 (2014)] recently found empirical formulas
relating the mass and surface redshift of nonrotating neutron stars to the
star's central density and to the parameter $\eta\equiv (K_0 L^2)^{1/3}$, where
$K_0$ is the incompressibility of symmetric nuclear matter and $L$ is the slope
of the symmetry energy at saturation density. Motivated by these
considerations, we extend the work by Sotani et al to slowly rotating and
tidally deformed neutron stars. We compute the moment of inertia, quadrupole
moment, quadrupole ellipticity, tidal and rotational Love number and apsidal
constant of slowly rotating neutron stars by integrating the Hartle-Thorne
equations at second order in rotation, and we fit all of these quantities as
functions of $\eta$ and of the central density. These fits may be used to
constrain $\eta$, either via observations of binary pulsars in the
electromagnetic spectrum, or via near-future observations of inspiralling
compact binaries in the gravitational-wave spectrum.
