Study of rational points on the elliptic curve

Authors

  • mariam alshatoury tishreen university
  • Hasan Sankari Tishreen University

Abstract

This research focused on  studying of a special type of curves given by non-singular  weierstrass equation which called elliptic curves, the study of elliptic curves had answered many of purely theoretical questions  asked by mathematicians , and it has great importance at the presenttime for its use inencryption,which depends on the algebraic structure of these curves ,so it has been the focus of attention of many recent studies.

One of the most important theorems is  Nagell-lutz theorem which used in the studying of elliptic curves since it is  a practical tool in finding all rational points of finite order on an elliptic curve over the rationals , the fundamental concepts were employed  in the theory of projective geometry including the theorem of bezout  to get the consequences of this study, this paper have focused on finding the rank of elliptic curves which has at least rational point of order two .

in addition to obtaining some important results related to these curves.

Downloads

Published

2024-06-08

How to Cite

1.
الشاتوري م, حسن سنكري. Study of rational points on the elliptic curve . TUJ-BA [Internet]. 2024Jun.8 [cited 2024Jul.3];46(2):25-38. Available from: https://journal.tishreen.edu.sy/index.php/bassnc/article/view/16833

Issue

Vol. 46 No. 2 (2024): Tishreen University Journal of Research and Scientific Studies - Basic Sciences Series

Section

Articles

License

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

The authors retain the copyright and grant the right to publish in the magazine for the first time with the transfer of the commercial right to the Tishreen University Journal -Basic Sciences Series  

 Under a CC BY- NC-SA 04 license that allows others to share the work with of the work's authorship and initial publication in this journal. Authors can use a copy of their articles in their scientific activity, and on their scientific websites, provided that the place of publication is indicted in Tishreen University Journal -Basic Sciences Series .  The Readers have the right to send, print and subscribe to the initial version of the article, and the title of Tishreen University Journal -Basic Sciences Series   Publisher

 

journal uses a CC BY-NC-SA license which mean

You are free to:

  • Adapt — remix, transform, and build upon the material
  •  
  • The licensor cannot revoke these freedoms as long as you follow the license terms.

 

  • Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
  • NonCommercial — You may not use the material for commercial purposes.
  • ShareAlike — If you remix, transform, or build upon the material, you must distribute your contributions under the same license as the original.
  • No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.