  Let $p$ and $q$ be distinct prime numbers, with $q\equiv 1\pmod{12}$. Let $N$
be a positive integer that is coprime to $pq$. We prove a formula relating the
Hasse--Weil zeta function of the modular curve $X_0(qN)_{\mathbb{F}_q}$ to the
Ihara zeta function of the $p$-isogeny graphs of supersingular elliptic curves
defined over $\overline{\mathbb{F}_q}$ equipped with a $\Gamma_0(N)$-level
structure. When $N=1$, this recovers a result of Sugiyama.
