Topics in elliptic curves.
مؤلف
Al-Marzouqiyah, Sheikha Abdullah.
الملخص الإنجليزي
The arithmetic of elliptic curves is an active research area. In the first part of this project we will give a full proof of Mordell's theorem which says that the set of rational points of an elliptic curve defined over rational numbers is a finitely generated abelian group. In the second part of the project we study the torsion subgroup of the group of rational points of an elliptic curve and give a detailed proof of Nagell-Lutz theorem. The third part of the project is devoted to study ranks of elliptic curves culminating in the formulation of the Birch and Swinnerton-Dyer conjecture.
