Lecture 1: Introduction to Elliptic Curves
Problem Set 1 out
Lecture 2: The Group Law and Weierstrass and Edwards Equations
Lecture 3: Finite Field Arithmetic
Problem Set 1 due
Problem Set 2 out
Lecture 4: Isogenies
Lecture 5: Isogeny Kernels and Division Polynomials
Problem Set 2 due
Problem Set 3 out
Lecture 6: Endomorphism Rings
Lecture 7: Hasse’s Theorem and Point Counting
Problem Set 3 due
Problem Set 4 out
Lecture 8: Schoof’s Algorithm
Lecture 9: Generic Algorithms for the Discrete Logarithm Problem
Problem Set 4 due
Problem Set 5 out
Lecture 10: Index Calculus, Smooth Numbers, and Factoring Integers
Problem Set 5 due
Lecture 11: Elliptic Curve Primality Proving (ECPP)
Problem Set 6 out
Lecture 12: Endomorphism Algebras
Problem Set 6 due
Lecture 13: Ordinary and Supersingular Curves
Problem Set 7 out
Lecture 14: Elliptic Curves over C (Part I)
Problem Set 7 due
Lecture 15: Elliptic Curves over C (Part II)
Problem Set 8 out
Lecture 16: Complex Multiplication (CM)
Lecture 17: The CM Torsor
Problem Set 8 due
Problem Set 9 out
Lecture 18: Riemann Surfaces and Modular Curves
Lecture 19: The Modular Equation
Problem Set 9 due
Problem Set 10 out
Lecture 20: The Hilbert Class Polynomial
Lecture 21: Ring Class Fields and the CM Method
Problem Set 10 due
Problem Set 11 out
Lecture 22: Isogeny Volcanoes
Lecture 23: The Weil Pairing
Problem Set 11 due
Problem Set 12 out
Lecture 24: Modular Forms and L-Functions
Lecture 25: Fermat’s Last Theorem
Problem Set 12 due
