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Elliptic Curves are related to the solutions to equations y^2 = x^3 + A x + B in the field of rationals, algebraic extensions of the rationals, p-adic rational numbers, or a finite field. They are used in factorization of integers and also played a role in the recent resolution of the conjecture known as Fermat's Last Theorem.

Fermat's Last Theorem	Software
Tables	Factoring
Primality Proving

• 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.
• Abstract Algebra Course notes by J.S. Milne. Topics covered are group, fields and Galois, algebraic number, class field theories. Other areas discussed are modular functions and forms, elliptic curves, algebraic geometry, Etale Cohomology, and Abelian varieties. In HTML, PDF, PostScript and DVI formats.
• 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.
• ECMNET Elliptic curve factoring software.
• ECMNET Project to factor numbers using the elliptic curve method. Client and server software.
• 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 Cryptology Marc Joye's list of resources that include 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 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.
• 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 R. E. Borcherds Including proof of the Moonshine Conjecture (TeX, DVI, PDF).
• Papers by Richard Borcherds Including proof of the Moonshine Conjecture (TeX,DVI,PDF).
• Pari Reference Cards On the home page of Joseph Silverman.
• 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.
• Silverman, Joseph Home page of mathematician at Brown University, with links to his publications and courses.
• 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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