See also:

• Science: Math: Number Theory: Diophantine Equations: Fermat's Last Theorem  (19)
• Science: Math: Number Theory: Factoring  (62)
• Science: Math: Number Theory: Prime Numbers: Primality Tests: Primality Proving  (12)

Algorithms for Modular Elliptic Curves - - Book by John Cremona, with introduction, tables and software.

Arithmetic of Cuves - - Papers and surveys by Ed Schaefer.

Bibliography for Automorphic and Modular Forms, L-Functions, Representations, and Number Theory - - Compiled by Paul Garrett, 1996.

The Birch and Swinnerton-Dyer Conjecture - - A Clay Mathematics Institute Prize problem, with description by Andrew Wiles [PDF] and lecture by Fernando Rodriguez-Villegas [.ram].

Counting Points on Elliptic Curves - - Robert Harley, Pierrick Gaudry, François Morain and Mireille Fouquet have established new records for point counting in characteristic 2, using a new algorithm by to Takakazu Satoh.

Course Notes - - Full notes as .dvi, .pdf, and .ps files for all the advanced courses J. S. Milne taught between 1986 and 1999.

ECDL Project - - Elliptic Curve Discrete Logarithms Project. They solved ECC2K-108 in April 2000. History and related papers.

ECMNET - - The ECMNET Project to find large factors by the Elliptic Curve Method, mainly Cunningham numbers.

An Elementary Introduction to Elliptic Curves - - By Len Charlap, David Robbins and Raymond Coley. Downloadable text in PostScript (.ps) format.

Elliptic Curves - - Links to research papers maintained by Stéfane Fermigier.

Elliptic Curves and Cryptology - - Marc Joye's list of elliptic curve resources includes people, books, and links. Many preprints are available from the site.

Elliptic Curves and Elliptic Functions - - Introductory notes by Charles Daney.

Elliptic Curves and Formal Groups - - Lecture notes from a seminar J. Lubin, J.-P. Serre and J. Tate.

Elliptic Curves and Right Triangles - - Slides (GIF) of lectures by Karl Rubin at Stanford University.

Elliptic Curves and Their Applications to Cryptography - - Web text by Andreas Enge.

Elliptic Curves Handout - - Syllabus and detailed reading list by Miles Reid, University of Warwick.

Elliptic Curves II - - Lecture notes by Johan P. Hansen.

Elliptic Curves with H. A. Verrill - - Lecture notes and resources by Helena Verrill, Louisiana State University, 2004.

Elliptic Divisibility Sequences - - Articles and links, compiled by Graham Everest.

Elliptic Functions and Elliptic Curves - - Lecture notes by Jan Nekovář (PS/PDF).

Elliptical Curve Cryptography - - Explains the difference between an elliptical curve and an ellipse. Discusses fields, applications, choosing a fixed point, and related topics.

Explicit Approaches to Modular Abelian Varieties - - William Stein, Ph.D. thesis, Berkeley, 2000.

14H52: Elliptic Curves - - From the Known Math series.

History of Elliptic Curve Rank Records - - A table up to rank 24 compiled by Andrej Dujella.

Iwasawa Theory of Elliptic Curves - - Lecture notes and surveys by Ralph Greenberg, University of Washington (PS).

Joseph Silverman - - Includes errata for his books Rational Points on Elliptic Curves and Advanced Topics in the Arithmetic of Elliptic Curves.

Kolyvagin Seminar - - A semester-long seminar studying Kolyvagin's application of Euler systems to elliptic curves. Includes extensive lecture notes in PostScript or DVI format.

Mathematical Things - - Tom Womack's pages address many elliptic curve subjects, including curves of given rank and small conductor, Mordell curves of large rank, and interesting torsion groups.

Modular Forms and Hecke Operators - - Notes by William A. Stein of a course by Ken Ribet.

Modular Forms Course - - Notes of a 1996 Berkeley course of Ken Ribet's on modular forms and Hecke operators.

Modular Forms Example Sheets - - From a course on modular forms.

Monstrous Moonshine - - the surprising and mysterious connections between the monster (and also other finite sporadic simple groups) and modular functions.

Moonshine Bibliography - - Books and papers relating to the Conway-Norton-Thompson Moonshine conjecture, proved by Richard Borcherds.

On 5 and 7 Descents for Elliptic Curves - - Tom Fisher's Ph.D. thesis (Cambridge, 2000) in DVI and PS format.

Papers by Richard Borcherds - - Including proof of the Moonshine Conjecture (TeX,DVI,PDF).

Prime Values of Elliptic Divisibility Sequences - - By Graham Everest.

A Proof of the Full Shimura-Taniyama-Weil Conjecture - - PDF-format article by Henri Darmon on the completion of the proof by Wiles, Breuil, Conrad, Diamond and Taylor.

Rational Points on Elliptic Curves - - A course by Jerrold Tunnell. An introduction to rational points on elliptic curves through examples.

Recent Progress in the Theory of Elliptic Curves - - An abstract to Henri Darmon's and Bertolini's work, which approaches a p-adic variant of the Birch - Swinnerton-Dyer conjecture, for curves of rank higher than one.

Richard Taylor - - Publications including the joint paper with Andrew Wiles which completed the proof of Fermat's Last Theorem.

Torsion Points on Elliptic Curves - - Elementary introduction and brief explanation of some well-known results.