Share This Article:

On the Torsion Subgroups of Certain Elliptic Curves over Q

Abstract Full-Text HTML Download Download as PDF (Size:157KB) PP. 304-308
DOI: 10.4236/apm.2013.32043    5,096 Downloads   7,592 Views  
Author(s)    Leave a comment

ABSTRACT

Let E be an elliptic curve over a given number field . By Mordells Theorem, the torsion subgroup of E defined over Q is a finite group. Using Lutz-Nagell Theorem, we explicitly calculate the torsion subgroup E(Q)tors for certain elliptic curves depending on their coefficients.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Y. Park, "On the Torsion Subgroups of Certain Elliptic Curves over Q," Advances in Pure Mathematics, Vol. 3 No. 2, 2013, pp. 304-308. doi: 10.4236/apm.2013.32043.

References

[1] B. Mazur, “Modular Curves and the Eisenstein Ideal,” Publications Mathématiques de l’Institut des Hautes études Scientifiques, No. 47, 1977, pp. 33-168.
[2] A. Knapp, “Elliptic Curves,” Princeton University Press, Princeton, 1992.
[3] D. Kim, J. K. Koo and Y. K. Park, “On the Elliptic Curves Modulo p,” Journal of Number Theory, Vol. 128, No. 4, 2008, pp. 945-953. doi:10.1016/j.jnt.2007.04.015

  
comments powered by Disqus

Copyright © 2018 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.