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Elliptic Curves and Modular Forms
Science: Math: Number Theory: Diophantine Equations: Fermat's Last Theorem
Science: Math: Number Theory: Factoring
Science: Math: Number Theory: Prime Numbers: Primality Tests: Primality Proving
14H52: Elliptic Curves
- From the Known Math series.
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.
- Full notes as .dvi, .pdf, and .ps files for all the advanced courses J. S. Milne taught between 1986 and 1999.
- Elliptic Curve Discrete Logarithms Project. They solved ECC2K-108 in April 2000. History and related papers.
- 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 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 Handout
- Syllabus and detailed reading list by Miles Reid, University of Warwick.
Elliptic Curves II
- Lecture notes by Johan P. Hansen.
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).
- Includes errata for his books Rational Points on Elliptic Curves and Advanced Topics in the Arithmetic of Elliptic Curves.
- A semester-long seminar studying Kolyvagin's application of Euler systems to elliptic curves. Includes extensive lecture notes in PostScript or DVI format.
- 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 Example Sheets
- From a course on modular forms.
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).
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. [PDF]
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.
- 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.
Elliptic Curves and Modular Forms
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