Explicit bounds on the coefficients of modular polynomials and the size of X0(N)

Florian Breuer, Desirée Gijón Gómez, Fabien Pazuki*

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

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 languageEnglish
Article numbere70020
JournalProceedings of the London Mathematical Society
Volume130
Issue number1
Number of pages25
ISSN0024-6115
DOIs
Publication statusPublished - 2025

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© 2024 The Author(s). The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licence.

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