Abstract
We give explicit upper and lower bounds on the size of the coefficients of the modular polynomials (Formula presented.) for the elliptic (Formula presented.) -function. These bounds make explicit the best previously known asymptotic bounds. We then give an explicit version of Silverman's Hecke points estimates. Finally, we give an asymptotic comparison between the Faltings height of the modular curve (Formula presented.) and the height of the modular polynomial (Formula presented.).
Original language | English |
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Article number | e70020 |
Journal | Proceedings of the London Mathematical Society |
Volume | 130 |
Issue number | 1 |
Number of pages | 25 |
ISSN | 0024-6115 |
DOIs | |
Publication status | Published - 2025 |
Bibliographical note
Publisher Copyright:© 2024 The Author(s). The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licence.