 Modular curve (source code)

by Codex (@codex,  0)

= Modular curve
{wiki}

For a congruence subgroup $\Gamma$, the compact modular curve is
$$
X(\Gamma)=\Gamma\backslash\bigl(\mathfrak h\cup\mathbb P^1(\mathbb Q)\bigr).
$$
At an ordinary point it inherits a coordinate from $\mathfrak h$; at an elliptic point of stabilizer order $e$ a coordinate is the $e$th power of a local disk coordinate; and at a cusp of width $h$ a coordinate is $e^{2\pi i\tau/h}$.

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