18.783 | Fall 2025 | Undergraduate

Elliptic Curves

Lecture Notes

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18.783 F25 Full Lecture Notes: Elliptic Curves
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18.783 F25 Lecture 01 Notes: Introduction to Elliptic Curves
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18.783 F25 Lecture 01 Slides: Introduction to Elliptic Curves
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18.783 F25 Lecture 02 Notes: Elliptic Curves as Abelian Groups
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18.783 F25 Lecture 03 Notes: Finite Field Arithmetic
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18.783 F25 Lecture 03 Slides: Finite Field Arithmetic
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18.783 F25 Lecture 04 Notes: Isogenies
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18.783 F25 Lecture 04 Slides: Isogenies
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18.783 F25 Lecture 05 Notes: Isogeny Kernels and Division Polynomials
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18.783 F25 Lecture 05 Slides: Isogeny Kernels and Division Polynomials
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18.783 F25 Lecture 06 Notes: Torsion Subgroups and Endomorphism Rings
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18.783 F25 Lecture 06 Slides: Torsion Subgroups and Endomorphism Rings
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18.783 F25 Lecture 07 Notes: Point Counting
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18.783 F25 Lecture 07 Slides: Point Counting
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18.783 F25 Lecture 08 Notes: Schoof’s Algorithm
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18.783 F25 Lecture 08 Slides: Schoof’s Algorithm
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18.783 F25 Lecture 09 Notes: The Discrete Logarithm Problem
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18.783 F25 Lecture 09 Slides: The Discrete Logarithm Problem
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18.783 F25 Lecture 10 Notes: Index Calculus, Smooth Numbers, and Factoring Integers
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18.783 F25 Lecture 10 Slides: Index Calculus, Smooth Numbers, and Factoring Integers
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18.783 F25 Lecture 11 Notes: Primality Proving
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18.783 F25 Lecture 11 Slides: Primality Proving
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18.783 F25 Lecture 12 Notes: Endomorphism Algebras
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18.783 F25 Lecture 12 Slides: Endomorphism Algebras
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18.783 F25 Lecture 13 Notes: Ordinary and Supersingular Elliptic Curves
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18.783 F25 Lecture 13 Slides: Ordinary and Supersingular Elliptic Curves
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18.783 F25 Lecture 14 Notes: Elliptic Curves over C (Part 1)
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18.783 F25 Lecture 14 Slides: Elliptic Curves over C (Part I)
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18.783 F25 Lecture 15 Notes: Elliptic Curves over C (Part 2)
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18.783 F25 Lecture 15 Slides: Elliptic Curves over C (Part II)
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18.783 F25 Lecture 16 Notes: Complex Multiplication (CM)
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18.783 F25 Lecture 16 Slides: Complex Multiplication (CM)
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18.783 F25 Lecture 17 Notes: The CM Torsor
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18.783 F25 Lecture 17 Slides: The CM Torsor
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18.783 F25 Lecture 18 Notes: Riemann Surfaces and Modular Curves
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18.783 F25 Lecture 18 Slides: Riemann Surfaces and Modular Curves
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18.783 F25 Lecture 19 Notes: The Modular Equation
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18.783 F25 Lecture 19 Slides: The Modular Equation
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18.783 F25 Lecture 20 Notes: The Hilbert Class Polynomial
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18.783 F25 Lecture 20 Slides: The Hilbert Class Polynomial
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18.783 F25 Lecture 21 Notes: Ring Class Fields and the CM Method
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18.783 F25 Lecture 21 Slides: Ring Class Fields and the CM Method
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18.783 F25 Lecture 22 Notes: Isogeny Volcanoes
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18.783 F25 Lecture 22 Slides: Isogeny Volcanoes
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18.783 F25 Lecture 23 Notes: Divisors and the Weil Pairing
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18.783 F25 Lecture 23 Slides: Divisors and the Weil Pairing
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18.783 F25 Lecture 24 Notes: Modular Forms and L-Functions
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18.783 F25 Lecture 24 Slides: Modular Forms and L-Functions
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18.783 F25 Lecture 25 Notes: Fermat’s Last Theorem
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18.783 F25 Lecture 25 Slides: Fermat’s Last Theorem

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Fall 2025

Level

Undergraduate

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