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Modular polynomials for the $j$-invariant
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Numbers
$n$ 
$\phi_n(x,y)$
INPUT{polynomials.yaml} (not shown in preview)
Definition
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.
Parameters
$n$
—   integer ($n \geq 1$)
Comments
(1)
More complete data is available at [3].
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)
Links
Data properties
Entries are of type: integral polynomial
Table is complete: no
Sources of data: [3], [1], [2]