Elliptic Curves

Calendar

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