18.783 | Fall 2025 | Undergraduate

Elliptic Curves

Lecture Notes

pdf
2 MB
18.783 F25 Full Lecture Notes: Elliptic Curves
pdf
323 kB
18.783 F25 Lecture 01 Notes: Introduction to Elliptic Curves
pdf
817 kB
18.783 F25 Lecture 01 Slides: Introduction to Elliptic Curves
pdf
390 kB
18.783 F25 Lecture 02 Notes: Elliptic Curves as Abelian Groups
pdf
632 kB
18.783 F25 Lecture 03 Notes: Finite Field Arithmetic
pdf
304 kB
18.783 F25 Lecture 03 Slides: Finite Field Arithmetic
pdf
499 kB
18.783 F25 Lecture 04 Notes: Isogenies
pdf
402 kB
18.783 F25 Lecture 04 Slides: Isogenies
pdf
543 kB
18.783 F25 Lecture 05 Notes: Isogeny Kernels and Division Polynomials
pdf
454 kB
18.783 F25 Lecture 05 Slides: Isogeny Kernels and Division Polynomials
pdf
449 kB
18.783 F25 Lecture 06 Notes: Torsion Subgroups and Endomorphism Rings
pdf
282 kB
18.783 F25 Lecture 06 Slides: Torsion Subgroups and Endomorphism Rings
pdf
456 kB
18.783 F25 Lecture 07 Notes: Point Counting
pdf
303 kB
18.783 F25 Lecture 07 Slides: Point Counting
pdf
439 kB
18.783 F25 Lecture 08 Notes: Schoof’s Algorithm
pdf
353 kB
18.783 F25 Lecture 08 Slides: Schoof’s Algorithm
pdf
548 kB
18.783 F25 Lecture 09 Notes: The Discrete Logarithm Problem
pdf
344 kB
18.783 F25 Lecture 09 Slides: The Discrete Logarithm Problem
pdf
563 kB
18.783 F25 Lecture 10 Notes: Index Calculus, Smooth Numbers, and Factoring Integers
pdf
375 kB
18.783 F25 Lecture 10 Slides: Index Calculus, Smooth Numbers, and Factoring Integers
pdf
432 kB
18.783 F25 Lecture 11 Notes: Primality Proving
pdf
300 kB
18.783 F25 Lecture 11 Slides: Primality Proving
pdf
432 kB
18.783 F25 Lecture 12 Notes: Endomorphism Algebras
pdf
266 kB
18.783 F25 Lecture 12 Slides: Endomorphism Algebras
pdf
411 kB
18.783 F25 Lecture 13 Notes: Ordinary and Supersingular Elliptic Curves
pdf
317 kB
18.783 F25 Lecture 13 Slides: Ordinary and Supersingular Elliptic Curves
pdf
481 kB
18.783 F25 Lecture 14 Notes: Elliptic Curves over C (Part 1)
pdf
310 kB
18.783 F25 Lecture 14 Slides: Elliptic Curves over C (Part I)
pdf
431 kB
18.783 F25 Lecture 15 Notes: Elliptic Curves over C (Part 2)
pdf
345 kB
18.783 F25 Lecture 15 Slides: Elliptic Curves over C (Part II)
pdf
378 kB
18.783 F25 Lecture 16 Notes: Complex Multiplication (CM)
pdf
299 kB
18.783 F25 Lecture 16 Slides: Complex Multiplication (CM)
pdf
423 kB
18.783 F25 Lecture 17 Notes: The CM Torsor
pdf
328 kB
18.783 F25 Lecture 17 Slides: The CM Torsor
pdf
462 kB
18.783 F25 Lecture 18 Notes: Riemann Surfaces and Modular Curves
pdf
383 kB
18.783 F25 Lecture 18 Slides: Riemann Surfaces and Modular Curves
pdf
382 kB
18.783 F25 Lecture 19 Notes: The Modular Equation
pdf
337 kB
18.783 F25 Lecture 19 Slides: The Modular Equation
pdf
462 kB
18.783 F25 Lecture 20 Notes: The Hilbert Class Polynomial
pdf
353 kB
18.783 F25 Lecture 20 Slides: The Hilbert Class Polynomial
pdf
500 kB
18.783 F25 Lecture 21 Notes: Ring Class Fields and the CM Method
pdf
338 kB
18.783 F25 Lecture 21 Slides: Ring Class Fields and the CM Method
pdf
429 kB
18.783 F25 Lecture 22 Notes: Isogeny Volcanoes
pdf
306 kB
18.783 F25 Lecture 22 Slides: Isogeny Volcanoes
pdf
495 kB
18.783 F25 Lecture 23 Notes: Divisors and the Weil Pairing
pdf
334 kB
18.783 F25 Lecture 23 Slides: Divisors and the Weil Pairing
pdf
556 kB
18.783 F25 Lecture 24 Notes: Modular Forms and L-Functions
pdf
432 kB
18.783 F25 Lecture 24 Slides: Modular Forms and L-Functions
pdf
496 kB
18.783 F25 Lecture 25 Notes: Fermat’s Last Theorem
pdf
295 kB
18.783 F25 Lecture 25 Slides: Fermat’s Last Theorem

Course Info

Departments
As Taught In
Fall 2025
Level
Undergraduate
Topics
Learning Resource Types
Lecture Notes
Open Textbooks
Problem Sets
Readings
Download Course
MIT Open Learning
Over 2,500 courses & materials
Freely sharing knowledge with learners and educators around the world. Learn more
© 2001–2026 Massachusetts Institute of Technology
Accessibility
Creative Commons License
Terms and Conditions
Proud member of:
© 2001–2026 Massachusetts Institute of Technology