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arXiv · 2610.25672

On The Manin Constant

Zhuoni Chi·Shurui Liu·Ping Nie
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Abstract

We prove the Manin constant conjecture for every optimal elliptic curve over $\mathbb{Q}$ and Stevens' Conjectures I and II. Our method adapts Hongbo Yin's congruence argument for cubic roots of modular functions to lifts of modular parametrizations through isogenies, using the unbounded denominators theorem of Calegari, Dimitrov and Tang.

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Zhuoni Chi, Shurui Liu, Ping Nie. 2026-10-19. On The Manin Constant. https://arxiv.org/abs/2610.25672

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