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We describe the neighborhood of the vertex $[E_0]$ (resp. $[E_{1728}]$) inthe $\ell$-isogeny graph $\mathcal{G}_\ell(\mathbb{F}_{p^2}, -2p)$ ofsupersingular 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.

Neighborhood of the supersingular elliptic curve isogeny graph at $j=0$ and $1728$