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Science: Math: Number_Theory: Elliptic_Curves_and_Modular_Forms

See also:




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.

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.

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