On the Torsion Subgroups of Certain Elliptic Curves over Q

ABSTRACT

Let * E *be an elliptic curve over a given number field . By Mordell’s 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.

Y. Park, "On the Torsion Subgroups of Certain Elliptic Curves over Q,"

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

[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