1 |
Introduction to Elliptic Curves |
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2 |
The Group Law, Weierstrass and Edwards Equations |
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3 |
Finite Fields and Integer Arithmetic |
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4 |
Finite Field Arithmetic |
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5 |
Isogenies |
Problem Set 1 Due |
6 |
Isogeny Kernels and Division Polynomials |
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7 |
Endomorphism Rings |
Problem Set 2 Due |
8 |
Hasse's Theorem, Point Counting |
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9 |
Schoof's Algorithm |
Problem Set 3 Due |
10 |
Generic Algorithms for Discrete Logarithms |
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11 |
Index Calculus, Smooth Numbers, Factoring Integers |
Problem Set 4 Due |
12 |
Elliptic Curve Primality Proving (ECPP) |
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13 |
Endomorphism Algebras |
Problem Set 5 Due |
14 |
Ordinary and Supersingular Curves |
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15 |
Elliptic Curves over C (Part 1) |
Problem Set 6 Due |
16 |
Elliptic Curves over C (Part 2) |
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17 |
Complex Multiplication |
Problem Set 7 Due |
18 |
The CM Torsor |
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19 |
Riemann Surfaces and Modular Curves |
Problem Set 8 Due |
20 |
The Modular Equation |
Problem Set 9 Due |
21 |
The Hilbert Class Polynomial |
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22 |
Ring Class Fields and the CM Method |
Problem Set 10 Due |
23 |
Isogeny Volcanoes |
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24 |
The Weil Pairing |
Problem Set 11 Due |
25 |
Modular Forms and L-series |
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26 |
Fermat's Last Theorem |
Problem Set 12 Due |