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.
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- ECMNET The ECMNET Project to find large factors by the Elliptic Curve Method, mainly Cunningham numbers.
- Course Notes Full notes as .dvi, .pdf, and .ps files for all the advanced courses J. S. Milne taught between 1986 and 1999.
- Papers by Richard Borcherds Including proof of the Moonshine Conjecture (TeX,DVI,PDF).
- Joseph Silverman Includes errata for his books Rational Points on Elliptic Curves and Advanced Topics in the Arithmetic of Elliptic Curves.
- Elliptic Curves and Formal Groups Lecture notes from a seminar J. Lubin, J.-P. Serre and J. Tate.
- 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.
- ECDL Project Elliptic Curve Discrete Logarithms Project. They solved ECC2K-108 in April 2000. History and related papers.
- Elliptic Curves II Lecture notes by Johan P. Hansen.
- Rational Points on Elliptic Curves A course by Jerrold Tunnell. An introduction to rational points on elliptic curves through examples.
- A Proof of the Full Shimura-Taniyama-Weil Conjecture Article by Henri Darmon on the completion of the proof by Wiles, Breuil, Conrad, Diamond and Taylor.
- 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.
- Bibliography for Automorphic and Modular Forms, L-Functions, Representations, and Number Theory Compiled by Paul Garrett, 1996.
- Iwasawa Theory of Elliptic Curves Lecture notes and surveys by Ralph Greenberg, University of Washington (PS).
- On 5 and 7 Descents for Elliptic Curves Tom Fisher's Ph.D. thesis (Cambridge, 2000) in DVI and PS format.
- Arithmetic of Cuves Papers and surveys by Ed Schaefer.
- History of Elliptic Curve Rank Records A table up to rank 24 compiled by Andrej Dujella.
- Elliptical Curve Cryptography Explains the difference between an elliptical curve and an ellipse. Discusses fields, applications, choosing a fixed point, and related topics.
- 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.
- Elliptic Functions and Elliptic Curves Lecture notes by Jan Nekovář (PS/PDF).
- 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.
- Torsion Points on Elliptic Curves Elementary introduction and brief explanation of some well-known results.
- Elliptic Curves Handout Syllabus and detailed reading list by Miles Reid, University of Warwick.
- Richard Taylor Publications including the joint paper with Andrew Wiles which completed the proof of Fermat's Last Theorem.
- Modular Forms Example Sheets From a course on modular forms.
- Algorithms for Modular Elliptic Curves Book by John Cremona, with introduction, tables and software.
- Explicit Approaches to Modular Abelian Varieties William Stein, Ph.D. thesis, Berkeley, 2000.
- Elliptic Curves and Elliptic Functions Introductory notes by Charles Daney.