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Reworded the title to be clearer

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edited Aug 25, 2021 at 0:16

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Is Are there only finitely many $m$ such that $m$ is the number of elliptic curves with a given conductor bounded?

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edited Aug 24, 2021 at 20:16

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Is the number of elliptic curves with a given conductor unboundedbounded?

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asked Aug 24, 2021 at 20:08

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Is the number of elliptic curves with a given conductor unbounded?

Let $f:\mathbb{N}\to\mathbb{N}$ be the map sending $n$ to the number of isomorphism classes of elliptic curves over $\mathbb{Q}$ with conductor $n$.

Is $f(\mathbb{N})$ finite?

ag.algebraic-geometry nt.number-theory