  If the observed quasi-periodic oscillations in magnetar flares are partially
confined to the crust, then the oscillation frequencies are unique probes of
the nuclear physics of the neutron star crust. We study crustal oscillations in
magnetars including corrections for a finite Alfven velocity. Our crust model
uses a new nuclear mass formula that predicts nuclear masses with an accuracy
very close to that of the finite range droplet model. This mass model for
equilibrium nuclei also includes shell corrections and an updated neutron-drip
line. We perturb our crust model to predict axial crust modes and assign them
to observed giant flare quasi-periodic oscillation frequencies from the soft
gamma-ray repeater SGR 1806-20. We find magnetar crusts that match observations
for various magnetic field strengths, entrainment of the free neutron gas in
the inner crust, and crust-core transition densities. We find that observations
can be reconciled with smaller values of the symmetry energy slope parameter,
L, if there is a significant amount of entrainment of the neutrons by the
superfluid or if the crust-core transition density is large. We also find
neutron star masses and radii which are in agreement with expectations from
what is known about low-density matter from nuclear experiment. Matching
observations with a field-free model we obtain the approximate values of M
=1.35 Msun and R = 11.9 km. Matching observations using a model with the
surface dipole field of SGR 1806-20 (B=2.4x10^15 G) we obtain the approximate
values of M = 1.25 Msun and R = 12.4 km.
