Modular invariants and isogenies

TY - JOUR

T1 - Modular invariants and isogenies

AU - Pazuki, Fabien

PY - 2019/4/1

Y1 - 2019/4/1

N2 - 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.

AB - 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.

U2 - 10.1142/S1793042119500295

DO - 10.1142/S1793042119500295

M3 - Journal article

SN - 1793-0421

SP - 1

EP - 16

JO - International Journal of Number Theory

JF - International Journal of Number Theory

ER -