14H52: Elliptic Curves
From the Known Math series. |
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. |
Algorithms for Modular Elliptic Curves
Book by John Cremona, with introduction, tables and software. |
An Elementary Introduction to Elliptic Curves
By Len Charlap, David Robbins and Raymond Coley. Downloadable text in PostScript (.ps) format. |
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. |
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. |
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. |
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. |
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. |
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]. |
Torsion Points on Elliptic Curves
Elementary introduction and brief explanation of some well-known results. |
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