On the Torsion Subgroups of Certain Elliptic Curves over Q


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.

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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.

Conflicts of Interest

The authors declare no conflicts of interest.


[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

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