Modular invariants and isogenies-Reference-Cited by-同舟云学术

Modular invariants and isogenies

Published:2019-03-21 Issue:03 Volume:15 Page:569-584
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

Pazuki Fabien¹

Affiliation:

1. Department of Mathematical Science, University of Copenhagen, Universitetsparken 5, Copenhagen 2100, Denmark

Abstract

We provide explicit bounds on the difference of heights of the [Formula: see text]-invariants of isogenous elliptic curves defined over [Formula: see text]. The first one is reminiscent of a classical estimate for the Faltings height of isogenous abelian varieties, which is indeed used in the proof. We also use an explicit version of Silverman’s inequality and isogeny estimates by Gaudron and Rémond. We give applications in the study of Vélu’s formulas and of modular polynomials.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793042119500295

Reference18 articles.

1. Hauteur des correspondances de Hecke

2. Ramanujan and the Modular j-Invariant

3. An explicit height bound for the classical modular polynomial

4. Class polynomials for nonholomorphic modular functions

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