Additional 5-divisibility conjecture for modular-polynomial coefficients

Let $ell$ be a prime with $0<m<ell$, and let $a_{ell,ell-m}$ be the coefficient of the $ell$-th classical modular polynomial $\Phi_ell(X,Y)$. Suppose one of the following holds: $ell\equiv 1$ or $3\pmod 5$ and $m\equiv 4\pmod 5$; $ell\equiv 2\pmod 5$ and $m\equiv 3\pmod 5$; or $ell\equiv 4\pmod 5$ and $m\equiv 2\pmod 5$. Additional 5-divisibility conjecture. Under these conditions, $5$ divides $a_{ell,ell-m}$. This extends the paper’s predicted 5-divisibility to cases not covered by the condition $ell+1>m+n$; the source offers it as a conjecture based on computations.