= Elliptic point of a modular curve
= Elliptic points of a modular curve
{synonym}
An <elliptic point of a modular curve> is the image of a point of the <complex upper half-plane> with a nontrivial <stabilizer subgroup> in the effective modular subgroup. For the full <modular group> the <stabilizer subgroup> orders are two and three, represented by $i$ and $e^{2\pi i/3}$. A local disk coordinate $u$ upstairs descends as $u^e$ when the <stabilizer subgroup> order is $e$. The central <matrices> $\pm I$ are factored out before counting this order.
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