  We construct an abelian quotient of the symplectic derivation Lie algebra
$\mathfrak{h}_{g,1}$ of the free Lie algebra generated by the fundamental
representation of $\mathrm{Sp}(2g,\mathbb{Q})$. More specifically, we show that
the weight $12$ part of the abelianization of $\mathfrak{h}_{g,1}$ is
$1$-dimensional for $g \ge 8$. The computation is done with the aid of
computers.
