Torsion groups of Mordell curves over number fields.

Abstract: Computing the torsion groups of elliptic curves defined over number fields is a classical topic and it has a vast literature in algebraic number theory. Any elliptic curve of the form $y^2 = x^3 + c$ is called Mordell curve. We know that the Mordell curve is a well-studied curve in the
family of CM-elliptic curves. 

In this talk, we will discuss the classification of torsion groups of rational Mordell Curves explicitly over cubic fields as well as over sextic fields. Also, we present the classification of  torsion groups of Mordell Curves over cubic fields. For Mordell curves over sextic fields, we provide all possible torsion groups. 

In the second part, we discuss torsion group of Mordell curves over higher degree number fields using some techniques of Galois representations.