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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 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 Curves: Links to research papers maintained by Stéfane Fermigier.
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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