Modular invariants and isogenies
Number Theory
2019-02-28 v5
Abstract
We provide explicit bounds on the difference of heights of the -invariants of isogenous elliptic curves defined over . 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 R\'emond. We give applications to the study of V\'elu's formulas and of modular polynomials.
Cite
@article{arxiv.1611.01094,
title = {Modular invariants and isogenies},
author = {Fabien Pazuki},
journal= {arXiv preprint arXiv:1611.01094},
year = {2019}
}