Explore: Elliptic Curves and Modular Forms, Number Theory
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 rol...
This page was last updated on October 3rd, 2008
This page was last updated on October 3rd, 2008
Elliptic Curves and Modular Forms (from Number Theory)
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Matt Baker's Papers
Mainly on elliptic curves.
Elliptic Curves and Formal Groups
Lecture notes from a seminar J. Lubin, J.-P. Serre and J. Tate.
Elliptic Curves and Elliptic Functions
Introductory notes by Charles Daney.
Modular Forms Example Sheets
From a course on modular forms.
Iwasawa Theory of Elliptic Curves
Lecture notes and surveys by Ralph Greenberg, University of Washington (PS).
Algorithms for Modular Elliptic Curves
Book by John Cremona, with introduction, tables and software.
ECMNET
The ECMNET Project to find large factors by the Elliptic Curve Method, mainly Cunningham numbers.
Modular Forms Course
Notes of a 1996 Berkeley course of Ken Ribet's on modular forms and Hecke operators.
Arithmetic of Cuves
Papers and surveys by Ed Schaefer.
Papers by Richard Borcherds
Including proof of the Moonshine Conjecture (TeX,DVI,PDF).
14H52: Elliptic Curves
From the Known Math series.
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.
Rational Points on Elliptic Curves
A course by Jerrold Tunnell. An introduction to rational points on elliptic curves through examples.
Moonshine Bibliography
Books and papers relating to the Conway-Norton-Thompson Moonshine conjecture, proved by Richard Borcherds.
Torsion Points on Elliptic Curves
Elementary introduction and brief explanation of some well-known results.
Joseph Silverman
Includes errata for his books Rational Points on Elliptic Curves and Advanced Topics in the Arithmetic of Elliptic Curves.
Elliptic Curves II
Lecture notes by Johan P. Hansen.
Modularity of Elliptic Curves and Beyond
Workshop, MSRI Berkeley, 6-10 December 1999.
Elliptic Curves Handout
Syllabus and detailed reading list by Miles Reid, University of Warwick.
Elliptic Curves and Right Triangles
Slides (GIF) of lectures by Karl Rubin at Stanford University.
Bibliography for Automorphic and Modular Forms, L-Functions, Representations, and Number Theory
Compiled by Paul Garrett, 1996.
Prime Values of Elliptic Divisibility Sequences
By Graham Everest.
Course Notes
Full notes as .dvi, .pdf, and .ps files for all the advanced courses J. S. Milne taught between 1986 and 1999.
Elliptic Curves
Links to research papers maintained by Stéfane Fermigier.
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.
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].
On 5 and 7 Descents for Elliptic Curves
Tom Fisher's Ph.D. thesis (Cambridge, 2000) in DVI and PS format.
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.
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.
Elliptic Curves and Cryptology
Marc Joye's list of elliptic curve resources includes people, books, and links. Many preprints are available from the site.
ECDL Project
Elliptic Curve Discrete Logarithms Project. They solved ECC2K-108 in April 2000. History and related papers.
An Elementary Introduction to Elliptic Curves
By Len Charlap, David Robbins and Raymond Coley. Downloadable text in PostScript (.ps) format.
Elliptical Curve Cryptography
Explains the difference between an elliptical curve and an ellipse. Discusses fields, applications, choosing a fixed point, and related topics.
Modular Curves X_0(N)
A series of lectures by Bas Edixhoven at the ICTP Summer school on rational torsion of elliptic curves over number fields.
Elliptic Curves and Their Applications to Cryptography
Web text by Andreas Enge.
Explicit Approaches to Modular Abelian Varieties
William Stein, Ph.D. thesis, Berkeley, 2000.
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.
History of Elliptic Curve Rank Records
A table up to rank 24 compiled by Andrej Dujella.
Modular Forms and Hecke Operators
Notes by William A. Stein of a course by Ken Ribet.
Monstrous Moonshine
the surprising and mysterious connections between the monster (and also other finite sporadic simple groups) and modular functions.
Elliptic Divisibility Sequences
Articles and links, compiled by Graham Everest.
Mainly on elliptic curves.
Lecture notes from a seminar J. Lubin, J.-P. Serre and J. Tate.
Introductory notes by Charles Daney.
From a course on modular forms.
Lecture notes and surveys by Ralph Greenberg, University of Washington (PS).
Book by John Cremona, with introduction, tables and software.
The ECMNET Project to find large factors by the Elliptic Curve Method, mainly Cunningham numbers.
Notes of a 1996 Berkeley course of Ken Ribet's on modular forms and Hecke operators.
Papers and surveys by Ed Schaefer.
Including proof of the Moonshine Conjecture (TeX,DVI,PDF).
From the Known Math series.
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.
A course by Jerrold Tunnell. An introduction to rational points on elliptic curves through examples.
Books and papers relating to the Conway-Norton-Thompson Moonshine conjecture, proved by Richard Borcherds.
Elementary introduction and brief explanation of some well-known results.
Includes errata for his books Rational Points on Elliptic Curves and Advanced Topics in the Arithmetic of Elliptic Curves.
Lecture notes by Johan P. Hansen.
Workshop, MSRI Berkeley, 6-10 December 1999.
Syllabus and detailed reading list by Miles Reid, University of Warwick.
Slides (GIF) of lectures by Karl Rubin at Stanford University.
Compiled by Paul Garrett, 1996.
By Graham Everest.
Full notes as .dvi, .pdf, and .ps files for all the advanced courses J. S. Milne taught between 1986 and 1999.
Links to research papers maintained by Stéfane Fermigier.
A semester-long seminar studying Kolyvagin's application of Euler systems to elliptic curves. Includes extensive lecture notes in PostScript or DVI format.
A Clay Mathematics Institute Prize problem, with description by Andrew Wiles [PDF] and lecture by Fernando Rodriguez-Villegas [.ram].
Tom Fisher's Ph.D. thesis (Cambridge, 2000) in DVI and PS format.
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.
PDF-format article by Henri Darmon on the completion of the proof by Wiles, Breuil, Conrad, Diamond and Taylor.
Marc Joye's list of elliptic curve resources includes people, books, and links. Many preprints are available from the site.
Elliptic Curve Discrete Logarithms Project. They solved ECC2K-108 in April 2000. History and related papers.
By Len Charlap, David Robbins and Raymond Coley. Downloadable text in PostScript (.ps) format.
Explains the difference between an elliptical curve and an ellipse. Discusses fields, applications, choosing a fixed point, and related topics.
A series of lectures by Bas Edixhoven at the ICTP Summer school on rational torsion of elliptic curves over number fields.
Web text by Andreas Enge.
William Stein, Ph.D. thesis, Berkeley, 2000.
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.
A table up to rank 24 compiled by Andrej Dujella.
Notes by William A. Stein of a course by Ken Ribet.
the surprising and mysterious connections between the monster (and also other finite sporadic simple groups) and modular functions.
Articles and links, compiled by Graham Everest.
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