In the post https://mathoverflow.net/questions/51147/what-objects-do-the-cusps-of-modular-curve-classify, it says that the fibers over the cusps of a modular curve are n-gons. Wikipedia (https://en.m.wikipedia.org/wiki/Modular_curve) says that the cusps are the orbits of $\mathbb{Q}\cup\infty$ under the action of the congruence subgroup. As a naive question, if we are working over $\mathbb{C}$, is it possible to tell what lies over a cusp by considering the orbit?
2026-03-27 16:55:12.1774630512
Generalized elliptic curves over cusps and orbits of $\mathbb{Q}\cup\infty$
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