Modular invariants and isogenies
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Modular invariants and isogenies. / Pazuki, Fabien.
In: International Journal of Number Theory, Vol. 15, No. 3, 2019, p. 569-584.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - Modular invariants and isogenies
AU - Pazuki, Fabien
PY - 2019
Y1 - 2019
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
VL - 15
SP - 569
EP - 584
JO - International Journal of Number Theory
JF - International Journal of Number Theory
SN - 1793-0421
IS - 3
ER -
ID: 215085325