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Let $N\\in\\{1,2,3,4,5,6,7,8,9,10,12,13,16,18,25\\},$ which are precisely the values for which the coarse moduli space of $\\mathcal{X}_0(N)$ is isomorphic to $\\mathbb{P}^1$. We show that the stacky Batyrev--Manin conjecture [DY24] holds for the naive height on $\\mathcal{X}_0(N)$ when $F=\\mathbb{Q}$. 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In the process, we give a concrete description of $\\mathcal{X}_0(N)$ as a square root stack over a stacky curve."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We show that the stacky Batyrev--Manin conjecture [DY24] holds for the naive height on X_0(N) when F=Q.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The listed values of N are precisely those for which the coarse moduli space of X_0(N) is isomorphic to P^1, and that the height in question is the naive height on the stack.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"The stacky Batyrev-Manin conjecture holds for naive heights on the modular stacks X_0(N) for N in {1,2,3,4,5,6,7,8,9,10,12,13,16,18,25} over 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