| Directory > Science > Math > Number Theory > Elliptic Curves and Modular Forms 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
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History of Elliptic Curve Rank Records
A table up to rank 24 compiled by Andrej Dujella.
http://www.math.hr/~duje/tors/rankhist.html
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Torsion Points on Elliptic Curves
Elementary introduction and brief explanation of some well-known results.
http://mat.uab.es/~xarles/elliptic.html
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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/
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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
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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
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Matt Baker's Papers
Mainly on elliptic curves.
http://www.math.berkeley.edu/~baker/papers.html
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Douglas Ulmer's Publications and Preprints
Mainly on elliptic curves and modular forms.
http://swc.math.arizona.edu/~ulmer/research/papers.html
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Iwasawa Theory of Elliptic Curves
Lecture notes and surveys by Ralph Greenberg, University of Washington (PS).
http://www.math.washington.edu/~greenber/research.html
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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
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Elliptic Curves and Elliptic Functions
Introductory notes by Charles Daney.
http://cgd.best.vwh.net/home/flt/flt03.htm
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Explicit Approaches to Modular Abelian Varieties
William Stein, Ph.D. thesis, Berkeley, 2000.
http://modular.fas.harvard.edu/papers/explicit/
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Elliptic Divisibility Sequences
Articles and links, compiled by Graham Everest.
http://www.mth.uea.ac.uk/~h090/EDS.html
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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/
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Prime Values of Elliptic Divisibility Sequences
By Graham Everest.
http://www.mth.uea.ac.uk/~h090/primeEDS.html
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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
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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
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Modularity of Elliptic Curves and Beyond
Workshop, MSRI Berkeley, 6-10 December 1999.
http://www.msri.org/activities/events/9900/hottopics/
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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
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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
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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/
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Modular Forms Example Sheets
From a course on modular forms.
http://www.math.berkeley.edu/~reb/modularforms/
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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
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14H52: Elliptic Curves
From the Known Math series.
http://www.math.niu.edu/~rusin/known-math/index/14H52.html
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Elliptic Curves Handout
Syllabus and detailed reading list by Miles Reid, University of Warwick.
http://www.maths.warwick.ac.uk/~miles/MA426/
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Satoh-FGH algorithm
Gonzalez and Harley explain Professor Satoh's elliptic curve point counting algorithm.
http://argote.ch/Research.html
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Papers by Richard Borcherds
Including proof of the Moonshine Conjecture (TeX,DVI,PDF).
http://www.math.berkeley.edu/~reb/papers/
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Elliptic Curves and Right Triangles
Slides (GIF) of lectures by Karl Rubin at Stanford University.
http://math.stanford.EDU/~rubin/lectures/sumo/
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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
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Elliptic Curves II
Lecture notes by Johan P. Hansen.
http://home.imf.au.dk/matjph/Ell-E99.html
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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
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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/
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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
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ECDL Project
Elliptic Curve Discrete Logarithms Project. They solved ECC2K-108 in April 2000. History and
related papers.
http://pauillac.inria.fr/~harley/ecdl/
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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
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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
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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/
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ECMNET
The ECMNET Project to find large factors by the Elliptic Curve Method, mainly Cunningham numbers.
http://www.loria.fr/~zimmerma/records/ecmnet.html
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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/
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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
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Elliptic Curves
Links to research papers maintained by Stéfane Fermigier.
http://www.fermigier.com/fermigier/elliptic.html.en
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