Modular invariants and isogenies

Research output: Contribution to journal › Journal article › Research › peer-review

Standard

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

Harvard

Pazuki, F 2019, 'Modular invariants and isogenies', International Journal of Number Theory, vol. 15, no. 3, pp. 569-584. https://doi.org/10.1142/S1793042119500295

APA

Pazuki, F. (2019). Modular invariants and isogenies. International Journal of Number Theory, 15(3), 569-584. https://doi.org/10.1142/S1793042119500295

Vancouver

Pazuki F. Modular invariants and isogenies. International Journal of Number Theory. 2019;15(3):569-584. https://doi.org/10.1142/S1793042119500295

Author

Pazuki, Fabien. / Modular invariants and isogenies. In: International Journal of Number Theory. 2019 ; Vol. 15, No. 3. pp. 569-584.

Bibtex

@article{483b1bd8da364c58bae78c2f95be1c77,
title = "Modular invariants and isogenies",
abstract = "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{\textquoteright}s inequality and isogeny estimates by Gaudron and R{\'e}mond. We give applications in the study of V{\'e}lu{\textquoteright}s formulas and of modular polynomials.",
author = "Fabien Pazuki",
year = "2019",
doi = "10.1142/S1793042119500295",
language = "English",
volume = "15",
pages = "569--584",
journal = "International Journal of Number Theory",
issn = "1793-0421",
publisher = "World Scientific Publishing Co. Pte. Ltd.",
number = "3",

}

RIS

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