  We describe the neighborhood of the vertex $[E_0]$ (resp. $[E_{1728}]$) in
the $\ell$-isogeny graph $\mathcal{G}_\ell(\mathbb{F}_{p^2}, -2p)$ of
supersingular elliptic curves over the finite field $\mathbb{F}_{p^2}$ when
$p>3\ell^2$ (resp. $p>4\ell^2$) with $E_0: y^2=x^3+1$ (resp. $E_{1728}:
y^2=x^3+x$) supersingular.
