Easiest way to distinguish $E_8 \oplus E_8$ from $E_{16}$

One of the possible tricks I was after was the following: the lattice generated by the roots (vectors of length $2$) of $E_8 \oplus E_8$ is $E_8 \oplus E_8$, whereas the lattice generated by the roots of $E_{16}$ is $D_{16}$ (which is of index $2$ in $E_{16}$).

Pari/gp has a very efficient way to list the roots. Putting the resulting matrix in Hermite normal form lets me see whether the index is $1$ or $2$.