18.783 | Spring 2021 | Undergraduate

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

Course Info

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As Taught In
Spring 2021
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Problem Sets
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