MIT OpenCourseWare

Browse materialsMIT 18.783 · Spring 2021

Elliptic Curves

Subjects: Algebra · Computer Science · Mathematics · Science

Art: Max Brückner (1860 – 1934), Brückner Vielflache Tafel 07 · Public domain

Instructor: Andrew V. Sutherland
Term: Spring 2021
Level: Undergraduate
What's inside: 12 problem sets · 1 lecture note · 1 reading · 46 other files · 6 web pages
Materials open: MIT OCW

Other versions of this course

18.783 · Fall 2025 · Study here
18.783 · Spring 2021 · Study here (this version)

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Start course: Lecture 1: Introduction to Elliptic Curves Find a topic

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About this course

Source: MIT OpenCourseWare 18.783 Elliptic Curves, Spring 2021, 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.

This course’s cited books, in our reading lists: Rational Points on Elliptic Curves · The Arithmetic of Elliptic Curves · Elliptic Curves · Advanced Topics in the Arithmetic of Elliptic Curves

How this course was organized

What's here, and what isn't

MIT's own materials here did not support a verified, course-wide order, so they are grouped by section instead.

Not included here

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MIT's page format for this item wasn't recognized clearly enough to place it safely. (53 items)

Materials by section

Grouped by section, as MIT organized them. Not sequenced or ordered.

Lecture Notes and Worksheets

34 files

Assignments

24 problem sets

2 images

MIT OpenCourseWare, Andrew V. Sutherland, 18.783 Elliptic Curves, Spring 2021.

License: CC BY-NC-SA 4.0 · Edition: Spring 2021 · Open the original course on OCW ↗

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Elliptic Curves

Before you start

What's here, and what isn't

Not included here

Materials by section

Lecture Notes and Worksheets

Assignments

Lecture 1: Introduction to Elliptic Curves

Lecture 2: The Group Law and Weierstrass and Edwards Equations

Lecture 3: Finite Field Arithmetic

Lecture 4: Isogenies

Lecture 5: Isogeny Kernels and Division Polynomials

Lecture 6: Endomorphism Rings

Lecture 7: Hasse’s Theorem and Point Counting

Lecture 8: Schoof’s Algorithm

Lecture 9: Generic Algorithms for the Discrete Logarithm Problem

Lecture 10: Index Calculus, Smooth Numbers, and Factoring Integers

Lecture 11: Elliptic Curve Primality Proving (ECPP)

Lecture 12: Endomorphism Algebras

Lecture 13: Ordinary and Supersingular Curves

Lecture 14: Elliptic Curves over C (Part I)

Lecture 15: Elliptic Curves over C (Part II)

Lecture 16: Complex Multiplication (CM)

Lecture 17: The CM Torsor

Lecture 18: Riemann Surfaces and Modular Curves

Lecture 19: The Modular Equation

Lecture 20: The Hilbert Class Polynomial

Lecture 21: Ring Class Fields and the CM Method

Lecture 22: Isogeny Volcanoes

Lecture 23: The Weil Pairing

Lecture 24: Modular Forms and L-Functions

Lecture 25: Fermat’s Last Theorem