The Mordell-Weil bases for the elliptic curve y 2 = x 3 - m 2 x + m 2

Sudhansu Sekhar Rout; Abhishek Juyal

Czechoslovak Mathematical Journal (2021)

  • Volume: 71, Issue: 4, page 1133-1147
  • ISSN: 0011-4642

Abstract

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Let D m be an elliptic curve over ℚ of the form y 2 = x 3 - m 2 x + m 2 , where m is an integer. In this paper we prove that the two points P - 1 = ( - m , m ) and P 0 = ( 0 , m ) on D m can be extended to a basis for D m ( ℚ ) under certain conditions described explicitly.

How to cite

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Rout, Sudhansu Sekhar, and Juyal, Abhishek. "The Mordell-Weil bases for the elliptic curve $y^2=x^3-m^2x+m^2$." Czechoslovak Mathematical Journal 71.4 (2021): 1133-1147. <http://eudml.org/doc/297526>.

@article{Rout2021,
abstract = {Let $D_m$ be an elliptic curve over $\mathbb \{Q\}$ of the form $y^2 = x^3 -m^2x +m^2$, where $m$ is an integer. In this paper we prove that the two points $P_\{-1\}=(-m, m)$ and $P_0 = (0, m)$ on $D_m$ can be extended to a basis for $D_m(\mathbb \{Q\})$ under certain conditions described explicitly.},
author = {Rout, Sudhansu Sekhar, Juyal, Abhishek},
journal = {Czechoslovak Mathematical Journal},
keywords = {elliptic curve; Mordell-Weil group; canonical height},
language = {eng},
number = {4},
pages = {1133-1147},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The Mordell-Weil bases for the elliptic curve $y^2=x^3-m^2x+m^2$},
url = {http://eudml.org/doc/297526},
volume = {71},
year = {2021},
}

TY - JOUR
AU - Rout, Sudhansu Sekhar
AU - Juyal, Abhishek
TI - The Mordell-Weil bases for the elliptic curve $y^2=x^3-m^2x+m^2$
JO - Czechoslovak Mathematical Journal
PY - 2021
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 71
IS - 4
SP - 1133
EP - 1147
AB - Let $D_m$ be an elliptic curve over $\mathbb {Q}$ of the form $y^2 = x^3 -m^2x +m^2$, where $m$ is an integer. In this paper we prove that the two points $P_{-1}=(-m, m)$ and $P_0 = (0, m)$ on $D_m$ can be extended to a basis for $D_m(\mathbb {Q})$ under certain conditions described explicitly.
LA - eng
KW - elliptic curve; Mordell-Weil group; canonical height
UR - http://eudml.org/doc/297526
ER -

References

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