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Genus 0 Modular curves of prime power level with a point defined over number fields other than ℚ

4 Aug 2022arXiv:2208.02452links table onlyarchive 2025-07-28

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Associated to an open subgroup G of GL₂(Zhat) satisfying conditions -I ∈G and det(G) ⊊(Zhat)^× there is a modular curve X_G which is a smooth compact curve defined over an extension of ℚ. In this article, we give a complete list of all such prime power level genus 0 modular curves with a point.

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