This is an archived course. A more recent version may be available at ocw.mit.edu.

Calendar

LEC # TOPICS KEY DATES
1 Introduction to Elliptic Curves  
2 The Group Law, Weierstrass and Edwards Equations  
3 Integer Arithmetic Problem Set 1 Due
4 Finite Field Arithmetic  
5 Isogenies and Endomorphisms Problem Set 2 Due
6 Division Polynomials and Torsion Subgroups  
7 Endomorphism Rings and Hasse's Theorem Problem Set 3 Due
8 Point Counting  
9 Schoof's Algorithm  
10 Discrete Logarithms: Generic Algorithms Problem Set 4 Due
11 Discrete Logarithms: Lower Bounds, Index Calculus  
12 Elliptic Curve Factorization Method (ECM) Problem Set 5 Due
13 Elliptic Curve Primality Proving (ECPP)  
14 Endomorphism Algebras Problem Set 6 Due
15 Ordinary and Supersingular Curves, The j-invariant  
16 Elliptic Functions, Eisenstein Series, Weierstrass p-function Problem Set 7 Due
17 Complex Tori, Elliptic Curves over C, Lattice j-invariants  
18 Uniformization Theorem, Complex Multiplication Problem Set 8 Due
19 Orders, Ideals, Class Groups, Isogenies over C  
20 Riemann Surfaces and the Modular Curve X(1) Problem Set 9 Due
21 Modular Functions and the Modular Equation  
22 The Main Theorem of Complex Multiplication Problem Set 10 Due
23 CM Method and Isogeny Volcanoes  
24 Modular Forms and L-functions Problem Set 11 Due
25 Fermat's Last Theorem Problem Set 12 Due