Elliptic Curves

Course content

The group law and Weierstrass equation. Isogenies. Torsion points and division polynomials. Elliptic curve over finite fields. Determining the group order. Schoof's algorithm. Elliptic curve primality proving. Elliptic curves over rational numbers. Mordell-Weil Theorem. Elliptic Curves over complex numbers. Complex multiplication. Integrality of j-invariants. Fermat's last theorem.