Explicit Methods for Modular Curves
Taught Course Centre (TCC)

Topics include:

• Galois representations of elliptic curves
• Classification of subgroups of GL_2(F_p)
• Modular curves and level structures, X(1), X_0(N), X_1(N), X_H
• Arithmetic of curves, Jacobians, Mordell-Weil groups
• The Eichler-Shimura theorem
• Equations for modular curves
• Sketch of Mazur's theorem on torsion of elliptic curves