Mordell

Mordell is a surname of English origin. In mathematical contexts, the name is associated with the study of elliptic curves and with several concepts named after the mathematician Louis Mordell, including the Mordell curve and the Mordell-Weil theorem.

The Mordell curve refers to the family of elliptic curves given by the equation y^2 = x^3 + k, where k is an integer. These curves are a subject of investigation in number theory, particularly regarding the distribution of rational solutions. They appear in various problems related to rational points on elliptic curves and have been studied to gain insights into the behavior of solutions across different values of k.

The Mordell-Weil theorem is a foundational result in the arithmetic of elliptic curves. It states that, for an elliptic curve defined over a number field, the group of its rational points forms a finitely generated abelian group. This structure allows the rational points to be described as a finite torsion subgroup together with a free abelian group of finite rank, providing a key tool for understanding the arithmetic of elliptic curves.

The name Mordell also appears in broader surname contexts; however, the mathematical terms associated with Mordell—Mordell curves and the Mordell-Weil theorem—are the most widely recognized usages in academic literature relating to elliptic curves and number theory.