Divisibility of the coefficients of modular polynomials

Let $N>1$ and let ΦN(X,Y)[X,Y] be the modular polynomial which vanishes precisely at pairs of j-invariants of elliptic curves linked by a cyclic isogeny of degree N. In this note we study the divisibility of the coefficients ΦN(X+J, Y+J) for certain algebraic numbers J, in particular $J=0$ and $J=1728$. It turns out that these coefficients are highly divisible by small primes at which J is supersingular.