Determines all modular curves with density degree five, suggesting further investigations at specific levels.
We determine all modular curves X 0 ( N ) X_0(N) with minimum density degree 5 5 , i.e. all curves X 0 ( N ) X_0(N) with infinitely many points of degree 5 5 and only finitely many points of degree d β€ 4 dβ€ 4 . As a consequence, the problem of determining all curves X 0 ( N ) X_0(N) with infinitely many points of degree 5 5 remains open for only 30 30 levels N N .
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Derickx et al. (2026) studied this question.
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