Modular invariants and isogenies

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningfagfællebedømt

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.
OriginalsprogEngelsk
TidsskriftInternational Journal of Number Theory
Vol/bind15
Udgave nummer3
Sider (fra-til)569-584
ISSN1793-0421
DOI
StatusUdgivet - 2019

ID: 215085325