Generators for the elliptic curve
Yasutsugu Fujita[1]; Nobuhiro Terai[2]
- [1] College of Industrial Technology Nihon University 2-11-1 Shin-ei, Narashino, Chiba 275–8576 Japan
- [2] Division of General Education Ashikaga Institute of Technology 268-1 Omae, Ashikaga, Tochigi 326–8558 Japan
Journal de Théorie des Nombres de Bordeaux (2011)
- Volume: 23, Issue: 2, page 403-416
- ISSN: 1246-7405
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topFujita, Yasutsugu, and Terai, Nobuhiro. "Generators for the elliptic curve $y^2=x^3-nx$." Journal de Théorie des Nombres de Bordeaux 23.2 (2011): 403-416. <http://eudml.org/doc/219816>.
@article{Fujita2011,
abstract = {Let $E$ be an elliptic curve given by $y^2=x^3-nx$ with a positive integer $n$. Duquesne in 2007 showed that if $n=(2k^2-2k+1)(18k^2+30k+17)$ is square-free with an integer $k$, then certain two rational points of infinite order can always be in a system of generators for the Mordell-Weil group of $E$. In this paper, we generalize this result and show that the same is true for infinitely many binary forms $n=n(k,l)$ in $\mathbb\{Z\}[k,l]$.},
affiliation = {College of Industrial Technology Nihon University 2-11-1 Shin-ei, Narashino, Chiba 275–8576 Japan; Division of General Education Ashikaga Institute of Technology 268-1 Omae, Ashikaga, Tochigi 326–8558 Japan},
author = {Fujita, Yasutsugu, Terai, Nobuhiro},
journal = {Journal de Théorie des Nombres de Bordeaux},
keywords = {elliptic curves},
language = {eng},
month = {6},
number = {2},
pages = {403-416},
publisher = {Société Arithmétique de Bordeaux},
title = {Generators for the elliptic curve $y^2=x^3-nx$},
url = {http://eudml.org/doc/219816},
volume = {23},
year = {2011},
}
TY - JOUR
AU - Fujita, Yasutsugu
AU - Terai, Nobuhiro
TI - Generators for the elliptic curve $y^2=x^3-nx$
JO - Journal de Théorie des Nombres de Bordeaux
DA - 2011/6//
PB - Société Arithmétique de Bordeaux
VL - 23
IS - 2
SP - 403
EP - 416
AB - Let $E$ be an elliptic curve given by $y^2=x^3-nx$ with a positive integer $n$. Duquesne in 2007 showed that if $n=(2k^2-2k+1)(18k^2+30k+17)$ is square-free with an integer $k$, then certain two rational points of infinite order can always be in a system of generators for the Mordell-Weil group of $E$. In this paper, we generalize this result and show that the same is true for infinitely many binary forms $n=n(k,l)$ in $\mathbb{Z}[k,l]$.
LA - eng
KW - elliptic curves
UR - http://eudml.org/doc/219816
ER -
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