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18.783 | Fall 2025 | Undergraduate

# Elliptic Curves

#### Course Description

This course offers a computationally focused introduction to elliptic curves, emphasizing their deep connections to number theory and cryptography. Core topics include point-counting, isogenies, pairings, and the theory of complex multiplication. Throughout the course, these concepts are applied to practical problems …
This course offers a computationally focused introduction to elliptic curves, emphasizing their deep connections to number theory and cryptography. Core topics include point-counting, isogenies, pairings, and the theory of complex multiplication. Throughout the course, these concepts are applied to practical problems such as integer factorization, primality proving, and elliptic curve cryptography.

## Course Info

##### Instructor

- Andrew V. Sutherland

##### Departments

- Mathematics

##### Topics

- Engineering
  - Computer Science
- Mathematics
  - Algebra and Number Theory
  - Computation

##### Learning Resource Types

notes Lecture Notes
menu_book Open Textbooks
assignment Problem Sets
auto_stories Readings
A 3-volcano of depth 2. (Image courtesy of Dr. Andrew Sutherland.)

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