APM  Vol.3 No.2 , March 2013
On the Torsion Subgroups of Certain Elliptic Curves over Q
Author(s) Yoon Kyung Park*
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.


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

 
 
Top