Torsion groups of elliptic curves over number fields

Abstract: Computing 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 a Mordell curve. Mordell curves are well studied elliptic curves with complex multiplication.

In this talk, for Mordell curves defined over the field of rational numbers we will discuss the classification of torsion groups over cubic and sextic fields. Also, we present the classification of torsion groups of Mordell curves defined over cubic fields. For Mordell curves over sextic fields, we provide all possible torsion groups. In the second part, we briefly discuss torsion groups of Mordell curves over higher degree number fields.

number theory

Audience: researchers in the topic

Warsaw Number Theory Seminar