  Nishiyama introduced a lattice theoretic classification of the elliptic
fibrations on a $K3$ surface. In a previous paper we used his method to exhibit
$52$ elliptic fibrations, up to isomorphisms, of the singular $K3$ surface of
discriminant $-12$. We prove here that the list is complete with a $53$th
fibration, thanks to a remark of Elkies and Sch\"{u}tt. We characterize the
fibration both theoretically and with a Weierstrass model.
