Dirichlet Structure Constant

$$\kappa(d)=\cases{ {2\ln\eta(d)\over\sqrt{d}} & for $d>0$\cr {2\pi\over w(d)\sqrt{\vert d\vert}} & for $d<0$,\cr}$$

where $\eta(d)$ is the Fundamental Unit and $w(d)$ is the number of substitutions which leave the binary quadratic form unchanged

$$w(d)=\cases{ 6 & for $d=-3$\cr 4 & for $d=-4$\cr 2 & otherwise.\cr}$$

See also Class Number, Dirichlet L-Series

References

Weisstein, E. W. ``Class Numbers.'' Mathematica notebook ClassNumbers.m.