Modular invariants and isogenies

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We provide explicit bounds on the difference of heights of the j-invariants of isogenous elliptic curves defined over Q¯¯¯¯. 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.
Original languageEnglish
JournalInternational Journal of Number Theory
Volume15
Issue number3
Pages (from-to)569-584
ISSN1793-0421
DOIs
Publication statusPublished - 2019

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