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.
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