  We explore high-pressure phase stability and superconductivity of lanthanum
hydrides $LaH_m$ (m=4-11,16). We predict stability of a hitherto unreported
polyhydride $P6/mmm$-$LaH_{16}$ at pressures above 150 GPa; at 200 GPa its
predicted superconducting $T_C$ is 156 K, critical field $\mu_0$$H_C$(0) ~ 35 T
and superconducting gap is up to 35 meV. We revisit superconductivity of the
recently discovered $LaH_{10}$ and find its $T_C$ to be up to 259 K (170 GPa)
from solving the Eliashberg equation and 271 K from solving the gap equation in
SCDFT which also allowed us to compute the Coulomb pseudopotential $\mu^*$ for
$LaH_{10}$ and $LaH_{16}$. Presence of several polymorph modifications of LaH10
may explain the variety in the experimentally measured $T_C$ values for
$LaH_{10}$ [1,2]
