8-dimensional 2-step nilpotent Lie algebras over algebraically closed fields of char $\mathrm{\ne }2,3$

We provide a self contained, elementary, and geometrically-flavored classification of $8$-dimensional $2$-step nilpotent Lie algebras over algebraically closed fields of characteristic $\mathrm{\ne }2,3$, using the algebro-geometric arguments from \cite{B} and elementary linear algebra.