Credits: 9

Type: advanced

Objectives:

Arithmetic of elliptical curves and the determination of their modularity; problem solving procedures for specific Diophantine problems.

Knowledge:

• Arithmetic of elliptical curves.
• Weierstrass equations. Addition law.
• Rational points on an elliptical curve.
• The Hasse-Weil L-function.
• Classical modular forms.
• Applications.

Subject-specific competences:

• To be able to use methods in arithmetic geometry for the treatment of Diophantine problems.
• To be able to test theorems in regard to rational points on elliptical curves: the Lutz-Nagell and Mordell theorems.
• To show understanding of classical modular forms and the Hasse-Weil L-function.
• To show understanding of Frey's elliptical curves and Fermat's last theorem.