Problem Sets · Problem Set
MIT OpenCourseWare
Elliptic Curves
Art: Max Brückner (1860 – 1934), Brückner Vielflache Tafel 07 · Public domain
- Instructor
- Andrew V. Sutherland
- Term
- Fall 2025
- Level
- Undergraduate
- What's inside
- 12 problem sets · 1 lecture note · 1 reading · 50 other files · 3 web pages
- Materials open
- MIT OCW
Other versions of this course
- 18.783 · Fall 2025 · Study here (this version)
- 18.783 · Spring 2021 · Study here
About this course
Source: MIT OpenCourseWare 18.783 Elliptic Curves, Fall 2025, Andrew V. Sutherland — original course page on ocw.mit.edu ↗. License: CC BY-NC-SA 4.0. Study order: MIT's own listing order, section by section. Taken from MIT's published course files, downloaded from ocw.mit.edu on September 23, 2026. How RedLectern is built.
Materials are grouped the way MIT organized them. A verified, course-wide order has not been established here.
Before you start
Prerequisites are not listed here. Check MIT's own syllabus for this course.
How this course was organized
What's here, and what isn't
- No lecture or session order could be confirmed for this course.
Not included here
62 items from the source could not be safely included:
- MIT's page format for this item wasn't recognized clearly enough to place it safely. (50 items)
- Found in the source, but not linked to a specific point in the course, so it isn't shown as an activity. (12 items)
Materials by section
Grouped by section, as MIT organized them. Not sequenced or ordered.
Lecture Notes and Worksheets
49 files
- 18.783 F25 Lecture 01 Notes: Introduction to Elliptic Curves Download
- 18.783 F25 Lecture 01 Slides: Introduction to Elliptic Curves Download
- 18.783 F25 Lecture 02 Notes: Elliptic Curves as Abelian Groups Download
- 18.783 F25 Lecture 03 Notes: Finite Field Arithmetic Download
- 18.783 F25 Lecture 03 Slides: Finite Field Arithmetic Download
- 18.783 F25 Lecture 04 Notes: Isogenies Download
- 18.783 F25 Lecture 04 Slides: Isogenies Download
- 18.783 F25 Lecture 05 Notes: Isogeny Kernels and Division Polynomials Download
- 18.783 F25 Lecture 05 Slides: Isogeny Kernels and Division Polynomials Download
- 18.783 F25 Lecture 06 Notes: Torsion Subgroups and Endomorphism Rings Download
- 18.783 F25 Lecture 06 Slides: Torsion Subgroups and Endomorphism Rings Download
- 18.783 F25 Lecture 07 Notes: Point Counting Download
- 18.783 F25 Lecture 07 Slides: Point Counting Download
- 18.783 F25 Lecture 08 Notes: Schoof’s Algorithm Download
- 18.783 F25 Lecture 08 Slides: Schoof’s Algorithm Download
- 18.783 F25 Lecture 09 Notes: The Discrete Logarithm Problem Download
- 18.783 F25 Lecture 09 Slides: The Discrete Logarithm Problem Download
- 18.783 F25 Lecture 10 Notes: Index Calculus, Smooth Numbers, and Factoring Integers Download
- 18.783 F25 Lecture 10 Slides: Index Calculus, Smooth Numbers, and Factoring Integers Download
- 18.783 F25 Lecture 11 Notes: Primality Proving Download
- 18.783 F25 Lecture 11 Slides: Primality Proving Download
- 18.783 F25 Lecture 12 Notes: Endomorphism Algebras Download
- 18.783 F25 Lecture 12 Slides: Endomorphism Algebras Download
- 18.783 F25 Lecture 13 Notes: Ordinary and Supersingular Elliptic Curves Download
- 18.783 F25 Lecture 13 Slides: Ordinary and Supersingular Elliptic Curves Download
- 18.783 F25 Lecture 14 Notes: Elliptic Curves over C (Part 1) Download
- 18.783 F25 Lecture 14 Slides: Elliptic Curves over C (Part I) Download
- 18.783 F25 Lecture 15 Notes: Elliptic Curves over C (Part 2) Download
- 18.783 F25 Lecture 15 Slides: Elliptic Curves over C (Part II) Download
- 18.783 F25 Lecture 16 Notes: Complex Multiplication (CM) Download
- 18.783 F25 Lecture 16 Slides: Complex Multiplication (CM) Download
- 18.783 F25 Lecture 17 Notes: The CM Torsor Download
- 18.783 F25 Lecture 17 Slides: The CM Torsor Download
- 18.783 F25 Lecture 18 Notes: Riemann Surfaces and Modular Curves Download
- 18.783 F25 Lecture 18 Slides: Riemann Surfaces and Modular Curves Download
- 18.783 F25 Lecture 19 Notes: The Modular Equation Download
- 18.783 F25 Lecture 19 Slides: The Modular Equation Download
- 18.783 F25 Lecture 20 Notes: The Hilbert Class Polynomial Download
- 18.783 F25 Lecture 20 Slides: The Hilbert Class Polynomial Download
- 18.783 F25 Lecture 21 Notes: Ring Class Fields and the CM Method Download
- 18.783 F25 Lecture 21 Slides: Ring Class Fields and the CM Method Download
- 18.783 F25 Lecture 22 Notes: Isogeny Volcanoes Download
- 18.783 F25 Lecture 22 Slides: Isogeny Volcanoes Download
- 18.783 F25 Lecture 23 Notes: Divisors and the Weil Pairing Download
- 18.783 F25 Lecture 23 Slides: Divisors and the Weil Pairing Download
- 18.783 F25 Lecture 24 Notes: Modular Forms and L-Functions Download
- 18.783 F25 Lecture 24 Slides: Modular Forms and L-Functions Download
- 18.783 F25 Lecture 25 Notes: Fermat’s Last Theorem Download
- 18.783 F25 Lecture 25 Slides: Fermat’s Last Theorem Download
Problem Sets
Course outline
Problem Sets · Problem Set
18.783 F25: Problem Set 02
Problem Sets · Problem Set
18.783 F25: Problem Set 03
Problem Sets · Problem Set
18.783 F25: Problem Set 04
Problem Sets · Problem Set
18.783 F25: Problem Set 05
Problem Sets · Problem Set
18.783 F25: Problem Set 06
Problem Sets · Problem Set
18.783 F25: Problem Set 07
Problem Sets · Problem Set
18.783 F25: Problem Set 08
Problem Sets · Problem Set
18.783 F25: Problem Set 09
Problem Sets · Problem Set
18.783 F25: Problem Set 10
Problem Sets · Problem Set
18.783 F25: Problem Set 11
Problem Sets · Problem Set
18.783 F25: Problem Set 12
MIT OpenCourseWare, Andrew V. Sutherland, 18.783 Elliptic Curves, Fall 2025.
License: CC BY-NC-SA 4.0 · Edition: Fall 2025 · Open the original course on OCW ↗
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