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.