Elliptic Curves and Modular Forms

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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 due 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.
» David Pollack - The author's thesis "Explicit Hecke Actions on Modular Forms, Harvard, 1998" is available here in DVI form.
» Douglas Ulmer's Publications and Preprints - Mainly on elliptic curves and modular forms.
» 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 Handout - Syllabus and detailed reading list by Miles Reid, University of Warwick.
» Elliptic Curves II - Lecture notes by Johan P. Hansen.
» 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 Divisibility Sequences - Articles and links, compiled by Graham Everest.
» 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.
» Matt Baker's Papers - Mainly on elliptic curves.
» Modular Curves X_0(N) - A series of lectures by Bas Edixhoven at the ICTP Summer school on rational torsion of elliptic curves over number fields.
» 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.
» Modular Forms and Hecke Operators - Notes by William A. Stein of a course by Ken Ribet.
» Modularity of Elliptic Curves and Beyond - Workshop, MSRI Berkeley, 6-10 December 1999.
» 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.
» Satoh-FGH algorithm - Gonzalez and Harley explain Professor Satoh's elliptic curve point counting algorithm.
» 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.