This table contains the first few classical modular polynomials $\phi_n(x,y) \in \mathbb{Z}[x,y]$, which vanish on the points $(j(n\tau),j(\tau))$, where $j$ denotes the $j$-invariant.
Every entry has been checked three ways: its degree in $x$ is $\psi(n)=n\prod_{p\mid n}(1+1/p)$, it is symmetric in $x$ and $y$ for $n>1$ and antisymmetric for $n=1$, and it vanishes at $(j(n\tau),j(\tau))$ evaluated at 2400 bits for three values of $\tau$. All twelve pass. The check was made after $\phi_1$ was found to read $x+y$, which vanishes on the diagonal only at $j=0$; it is $x-y$, and it was the only entry that was wrong.
References
[1]
Reinier Broker, Kristin Lauter, Andrew V. Sutherland, "Modular polynomials via isogeny volcanoes", Mathematics of Computation 81 (2012), 1201-1231. (arXiv)
[2]
Jan Hendrik Bruinier, Ken Ono, Andrew V. Sutherland, "Class polynomials for nonholomorphic modular functions", Journal of Number Theory 161 (2016) 204-229. (arXiv)