  We compute the critical $L$-values of some weight 3, 4, or 5 modular forms,
by transforming them into integrals of the complete elliptic integral $K$. In
doing so, we prove closed form formulas for some moments of $K'^3$. Many of our
$L$-values can be expressed in terms of Gamma functions, and this also gives
new lattice sum evaluations.
