# |
Date |
Topic (references) |
Materials |

1 | 2/6 | Introduction | **slides** |

2 | 2/11 | The group law, Weierstrass and Edwards equations (**Washington** 2.1-3, 2.6.3, **Bernstein-Lange**) | **notes**, **worksheet 1**, **worksheet 2** |

3 | 2/13 | Finite fields and integer arithmetic (**Modern Computer Algebra** Ch. 8) | **notes** |

4 | 2/19 | Finite field arithmetic (**Modern Computer Algebra**: Sec. 3.2, 9.1, 11.1, **HEHCC** Ch. 9, **Rabin**) | **notes** |

5 | 2/20 | Isogenies (**Washington** 2.9, **Silverman** III.4) | **notes** |

6 | 2/25 | Isogeny kernels and division polynomials (**Washington** 3.2, 12.3, **Silverman** III.4)) | **notes**, **worksheet** |

7 | 2/27 | Endomorphism rings (**Washington** 4.2, , **Silverman** III.6) | **notes** |

8 | 3/4 | Hasse's Theorem, point counting (**Washington** 4.3) | **notes** |

9 | 3/6 | Schoof's algorithm (**Washington** 4.2, 4.5, **Schoof**) | **notes**, **worksheet** |

10 | 3/11 | Generic algorithms for discrete logarithms (**Washington** 5.2, **Pohlig-Hellman**, **Pollard**, **Shoup**) | **notes** |

11 | 3/13 | Index calculus, smooth numbers, factoring integers (**Washington** 5.1, 7.1, **Granville**, **Lenstra**) | **notes**, **worksheet 1**, **worksheet 2**, **worksheet 3** |

12 | 3/15 | Elliptic curve primality proving (ECPP) (**Washington** 7.2, **Goldwasser-Kilian**, **Pomerance**) | **notes** |

13 | 3/22 | Endomorphism algebras (**Silverman** III.9) | **notes** |

14 | 4/1 | Ordinary and supersingular curves (**Silverman** III.1,V, **Washington** 2.7, 4.6) | **notes** |

15 | 4/3 | Elliptic curves over C (part I) (**Cox** Sec. 10, **Silverman** VI.2-3, **Washington** 9.1-2) | **notes** |

16 | 4/8 | Elliptic curves over C (part II) (**Cox** Sec. 10-11, **Silverman** VI.4-5, **Washington** 9.2-3) | **notes** |

17 | 4/10 | Complex multiplication (CM) (**Cox** Sec. 11, **Silverman** VI.5, **Washington** 9.3) | **notes** |

18 | 4/17 | The CM torsor (**Cox** Sec. 7, **Silverman (advanced topics)** II.1.1) | **notes** |

19 | 4/22 | Riemann surfaces and modular curves (**Silverman (advanced topics)** I.2, **Milne** V.1) | **notes** |

20 | 4/24 | The modular equation (**Cox** Sec. 11, **Milne** V.2, **Washington** pp. 273-274) | **notes** |

21 | 4/29 | The Hilbert class polynomial (**Cox** Sec. 8, 11) | **notes** |

22 | 5/1 | Ring class fields and the CM method (**Cox** 8, 11) | **notes** |

23 | 5/6 | Isogeny volcanoes (**Sutherland**) | **notes** |

24 | 5/8 | The Weil pairing (**Miller**, **Washington** 11, **Silverman** III.8) | **notes** |

25 | 5/13 | Modular forms and L-series (**Milne** V.3-4) | **notes** |

26 | 5/15 | Fermat's last theorem (**Milne** V.7-9, **Washington** 15, **Cornell-Stevens-Silverman** I) | **notes** |