Fourth Edition of the International Conference on Research in Applied Mathematics and Computer Science ICRAMCS 2022
 March 24-25-26, 2022
Online and Face-to-Face Conference

ICRAMCS, 4 (2022) | Proceedings ISSN: 2605-7700

Research Communication | Open Access
Volume 2022 | Communication ID 466
Torsion Section of Elliptic curves over the Ring Q[e], e^2=e.
Zakariae Cheddour, Abdelhakim Chillali, Ali Mouhib
Academic Editor: Youssef EL FOUTAYENI
Received
Accepted
Published
January 31, 2022
March 03, 2388
April 15, 2388

Abstract: Let E be an elliptic curve over Q. Mazur[4] has classified the torsion group of an elliptic curve on Q. Since the work on torsion groups has been developed by several mathematicians, we have in [1,2,3] the classifications of the torsion group over quadratic extensions of Q, and [5,6] for quadratic cyclotomic fields. In this paper, we will study the torsion section of elliptic curves on the ring L=Q[e] with e^2=e. We take a different approach for this ring by first establishing an isomorphism between the elliptic curve given by a Weierstrass equation Y^2 Z=X^3+aXZ^2+bZ^3over L, and ...