  Extending investigations of Barker, Humpherys, Lafitte, Rudd, and Zumbrun for
compressible gas dynamics and Freist\"uhler and Trakhinin for compressible
magnetohydrodynamics, we study by a combination of asymptotic ODE estimates and
numerical Evans function computations the one-dimensional stability of parallel
isentropic magnetohydrodynamic shock layers over the full range of physical
parameters (shock amplitude, strength of imposed magnetic field, viscosity,
magnetic permeability, and electrical resistivity) for a $\gamma$-law gas with
$\gamma\in [1,3]$. Other $\gamma$-values may be treated similarly, but were not
checked numerically. Depending on magnetic field strength, these shocks may be
of fast Lax, intermediate (overcompressive), or slow Lax type; however, the
shock layer is independent of magnetic field, consisting of a purely
gas-dynamical profile. In each case, our results indicate stability.
Interesting features of the analysis are the need to renormalize the Evans
function in order to pass continuously across parameter values where the shock
changes type or toward the large-amplitude limit at frequency $\lambda=0$ and
the systematic use of winding number computations on Riemann surfaces.
