Science Math Number Theory Elliptic Curves and Modular Forms

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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Algorithms for Modular Elliptic Curves
Book by John Cremona, with introduction, tables and software.
Arithmetic of Cuves
Papers and surveys by Ed Schaefer.
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.
The ECMNET Project to find large factors by the Elliptic Curve Method, mainly Cunningham numbers.
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).
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 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.
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.
[Mozilla Einstein]
Last update:
August 25, 2016 at 5:45:10 UTC
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