Study of rational points on the elliptic curve
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.
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