A parametrised family of Mordell curves with a rational point of order 3

Abstract

An elliptic curve defined by an equation of the type y 2 = x 3 + d is called a Mordell curve. We obtain a parametrised family of Mordell curves whose rank, in general, is at least three, and whose torsion group is Z/3Z.

Families of Mordell Curves with Non-trivial Torsion and Rank of at Least Three

“…The elliptic curve represented by ( 1) is known as a Mordell curve. Choudry and Zargar [1] obtained a parametrized family of Mordell curves with the rank of at least three. They obtained the solution using a quadratic system of equations.…”