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Atkin Modular Polynomial Database
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The Atkin modular function $f(q)$ of prime level N is a modular function
on $X_0^+(N)$ of minimal degree, holomorphic on the upper half plane, and whose
$q$-expansion has leading coefficient $1$. It is unique up to a constant.
The Atkin modular polynomial is a bivariate polynomial $\Phi_N(X,Y)$ such
that
$$
\Phi_N(f(q),j(q)) = 0,
$$
where $j(q) = q^{-1} + 744 + 196884 q + \cdots$ is the modular $j$-invariant.
Since $f(q)$ is invariant under the Atkin-Lehner operator, and the image of
$j(q)$ is $j_N(q) = j(q^N)$, we also have $\Phi_N(f(q),j_N(q)) = 0$.
Levels
Degrees