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 |

## Calendar

## Course Info

##### Instructor

##### Departments

##### As Taught In

Spring
2021

##### Level

##### Learning Resource Types

*assignment*Problem Sets

*notes*Lecture Notes

*Instructor Insights*