When I read about famous lattices ($E_8$, Leech, ...) I always only see listed the norm of their shortest vectors. However, I am interested in the norm of the second shortest vectors (and if possible, also the norm of the $n$-shortest vectors).
I am not interested in computing these for arbitrary lattices, but I want to know of a reference that tabulates these norms for the most important lattices, or learn of a way to compute these norms from the other data usually given for such lattices.