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Elliptic Curves and Modular Forms
Directory > Science > Math > Number Theory > Elliptic Curves and Modular Forms

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Software (11) Tables (17)

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Elliptical Curve Cryptography
Explains the difference between an elliptical curve and an ellipse. Discusses fields,
applications, choosing a fixed point, and related topics.

http://www.cryptoman.com/elliptic.htm
Reviews Rating: Not yet Rated Whois Check

History of Elliptic Curve Rank Records
A table up to rank 24 compiled by Andrej Dujella.
http://www.math.hr/~duje/tors/rankhist.html
Reviews Rating: Not yet Rated Whois Check

Torsion Points on Elliptic Curves
Elementary introduction and brief explanation of some well-known results.
http://mat.uab.es/~xarles/elliptic.html
Reviews Rating: Not yet Rated Whois Check

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].

http://www.claymath.org/Millennium_Prize_Problems/Birch_and_Swinnerton-Dyer_Conjecture/
Reviews Rating: Not yet Rated Whois Check

An Elementary Introduction to Elliptic Curves
By Len Charlap, David Robbins and Raymond Coley. Downloadable text in PostScript (.ps) format.
http://www.idaccr.org/reports/reports.html
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Arithmetic of Cuves
Papers and surveys by Ed Schaefer.
http://math.scu.edu/~eschaefe/nt.html
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Richard Taylor
Publications including the joint paper with Andrew Wiles which completed the proof of Fermat's Last
Theorem.

http://www.math.harvard.edu/~rtaylor/
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Modular Forms and Hecke Operators
Notes by William A. Stein of a course by Ken Ribet.
http://modular.fas.harvard.edu/MF.html
Reviews Rating: Not yet Rated Whois Check

On 5 and 7 Descents for Elliptic Curves
Tom Fisher's Ph.D. thesis (Cambridge, 2000) in DVI and PS format.
http://www.dpmms.cam.ac.uk/~taf1000/thesis.html
Reviews Rating: Not yet Rated Whois Check

Matt Baker's Papers
Mainly on elliptic curves.
http://www.math.berkeley.edu/~baker/papers.html
Reviews Rating: Not yet Rated Whois Check

Douglas Ulmer's Publications and Preprints
Mainly on elliptic curves and modular forms.
http://swc.math.arizona.edu/~ulmer/research/papers.html
Reviews Rating: Not yet Rated Whois Check

Iwasawa Theory of Elliptic Curves
Lecture notes and surveys by Ralph Greenberg, University of Washington (PS).
http://www.math.washington.edu/~greenber/research.html
Reviews Rating: Not yet Rated Whois Check

Moonshine Bibliography
Books and papers relating to the Conway-Norton-Thompson Moonshine conjecture, proved by Richard
Borcherds.

http://cicma.concordia.ca/faculty/cummins/moonshine.refs.html
Reviews Rating: Not yet Rated Whois Check

Elliptic Curves and Elliptic Functions
Introductory notes by Charles Daney.
http://cgd.best.vwh.net/home/flt/flt03.htm
Reviews Rating: Not yet Rated Whois Check

Explicit Approaches to Modular Abelian Varieties
William Stein, Ph.D. thesis, Berkeley, 2000.
http://modular.fas.harvard.edu/papers/explicit/
Reviews Rating: Not yet Rated Whois Check

Elliptic Divisibility Sequences
Articles and links, compiled by Graham Everest.
http://www.mth.uea.ac.uk/~h090/EDS.html
Reviews Rating: Not yet Rated Whois Check

Modular Forms Course
Notes of a 1996 Berkeley course of Ken Ribet's on modular forms and Hecke operators.
http://modular.fas.harvard.edu/Tables/Notes/
Reviews Rating: Not yet Rated Whois Check

Prime Values of Elliptic Divisibility Sequences
By Graham Everest.
http://www.mth.uea.ac.uk/~h090/primeEDS.html
Reviews Rating: Not yet Rated Whois Check

Bibliography for Automorphic and Modular Forms, L-Functions, Representations, and Number Theory
Compiled by Paul Garrett, 1996.
http://www.math.umn.edu/~garrett/m/b/bib.html
Reviews Rating: Not yet Rated Whois Check

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.

http://www.cms.math.ca/CMS/Events/winter98/w98-abs/node2.html
Reviews Rating: Not yet Rated Whois Check

Modularity of Elliptic Curves and Beyond
Workshop, MSRI Berkeley, 6-10 December 1999.
http://www.msri.org/activities/events/9900/hottopics/
Reviews Rating: Not yet Rated Whois Check

Monstrous Moonshine
the surprising and mysterious connections between the monster (and also other finite sporadic
simple groups) and modular functions.

http://cicma.concordia.ca/faculty/cummins/moonshine.html
Reviews Rating: Not yet Rated Whois Check

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.

http://www.ams.org/notices/199911/comm-darmon.pdf
Reviews Rating: Not yet Rated Whois Check

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.

http://www-math.mit.edu/~osserman/seminar/
Reviews Rating: Not yet Rated Whois Check

Modular Forms Example Sheets
From a course on modular forms.
http://www.math.berkeley.edu/~reb/modularforms/
Reviews Rating: Not yet Rated Whois Check

Algorithms for Modular Elliptic Curves
Book by John Cremona, with introduction, tables and software.
http://www.maths.nott.ac.uk/personal/jec/book/chapter1.html
Reviews Rating: Not yet Rated Whois Check

14H52: Elliptic Curves
From the Known Math series.
http://www.math.niu.edu/~rusin/known-math/index/14H52.html
Reviews Rating: Not yet Rated Whois Check

Elliptic Curves Handout
Syllabus and detailed reading list by Miles Reid, University of Warwick.
http://www.maths.warwick.ac.uk/~miles/MA426/
Reviews Rating: Not yet Rated Whois Check

Satoh-FGH algorithm
Gonzalez and Harley explain Professor Satoh's elliptic curve point counting algorithm.
http://argote.ch/Research.html
Reviews Rating: Not yet Rated Whois Check

Papers by Richard Borcherds
Including proof of the Moonshine Conjecture (TeX,DVI,PDF).
http://www.math.berkeley.edu/~reb/papers/
Reviews Rating: Not yet Rated Whois Check

Elliptic Curves and Right Triangles
Slides (GIF) of lectures by Karl Rubin at Stanford University.
http://math.stanford.EDU/~rubin/lectures/sumo/
Reviews Rating: Not yet Rated Whois Check

Rational Points on Elliptic Curves
A course by Jerrold Tunnell. An introduction to rational points on elliptic curves through
examples.

http://www.math.rutgers.edu/~tunnell/math574.html
Reviews Rating: Not yet Rated Whois Check

Elliptic Curves II
Lecture notes by Johan P. Hansen.
http://home.imf.au.dk/matjph/Ell-E99.html
Reviews Rating: Not yet Rated Whois Check

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.

http://www.maths.univ-rennes1.fr/~edix/cours/trieste.html
Reviews Rating: Not yet Rated Whois Check

David Pollack
The author's thesis "Explicit Hecke Actions on Modular Forms, Harvard, 1998" is available
here in DVI form.

http://www.math.ohio-state.edu/~pollack/
Reviews Rating: Not yet Rated Whois Check

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 due to Takakazu Satoh.

http://www.lix.polytechnique.fr/Labo/Mireille.Fouquet/elliptic.html
Reviews Rating: Not yet Rated Whois Check

ECDL Project
Elliptic Curve Discrete Logarithms Project. They solved ECC2K-108 in April 2000. History and
related papers.

http://pauillac.inria.fr/~harley/ecdl/
Reviews Rating: Not yet Rated Whois Check

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.

http://tom.womack.net/maths/maths.htm
Reviews Rating: Not yet Rated Whois Check

Elliptic Curves and Cryptology
Marc Joye's list of elliptic curve resources includes people, books, and links. Many preprints are
available from the site.

http://www.geocities.com/marcjoye/biblio_ell.html
Reviews Rating: Not yet Rated Whois Check

Course Notes
Full notes as .dvi, .pdf, and .ps files for all the advanced courses J. S. Milne taught between
1986 and 1999.

http://www.jmilne.org/math/CourseNotes/
Reviews Rating: Not yet Rated Whois Check

ECMNET
The ECMNET Project to find large factors by the Elliptic Curve Method, mainly Cunningham numbers.
http://www.loria.fr/~zimmerma/records/ecmnet.html
Reviews Rating: Not yet Rated Whois Check

Joseph Silverman
Includes errata for his books Rational Points on Elliptic Curves and Advanced Topics in the
Arithmetic of Elliptic Curves.

http://www.math.brown.edu/~jhs/
Reviews Rating: Not yet Rated Whois Check

Elliptic Curves and Formal Groups
Lecture notes from a seminar J. Lubin, J.-P. Serre and J. Tate.
http://www.ma.utexas.edu/users/voloch/lst.html
Reviews Rating: Not yet Rated Whois Check

Elliptic Curves
Links to research papers maintained by Stéfane Fermigier.
http://www.fermigier.com/fermigier/elliptic.html.en
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