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Elliptic Curves and Modular Forms
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Web Pages
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  http://www.loria.fr/~zimmerma/records/ecmnet.html http://www.loria.fr/~zimmerma/records/ecmnet.html
The ECMNET Project to find large factors by the Elliptic Curve Method, mainly Cunningham numbers.
  Elliptic Curves http://www.fermigier.com/fermigier/elliptic.html.en
Links to research papers maintained by Stéfane Fermigier.
  The Birch and Swinnerton-Dyer Conjecture http://www.claymath.org/millennium/Birch_and_Swinnerton-Dyer_Conjecture/
A Clay Mathematics Institute Prize problem, with description by Andrew Wiles [PDF] and lecture by Fernando Rodriguez-Villegas [.ram].
  Joseph Silverman http://www.math.brown.edu/~jhs/
Includes errata for his books Rational Points on Elliptic Curves and Advanced Topics in the Arithmetic of Elliptic Curves.
  An Elementary Introduction to Elliptic Curves http://www.idaccr.org/reports/reports.html
By Len Charlap, David Robbins and Raymond Coley. Downloadable text in PostScript (.ps) format.
  Bibliography for Automorphic and Modular Forms, L-Functions, Representations, and Number Theory http://www.math.umn.edu/~garrett/m/b/bib.html
Compiled by Paul Garrett, 1996.
  ECDL Project http://pauillac.inria.fr/~harley/ecdl/
Elliptic Curve Discrete Logarithms Project. They solved ECC2K-108 in April 2000. History and related papers.
  Richard Taylor http://www.math.harvard.edu/~rtaylor/
Publications including the joint paper with Andrew Wiles which completed the proof of Fermat's Last Theorem.
  Course Notes http://www.jmilne.org/math/CourseNotes/
Full notes as .dvi, .pdf, and .ps files for all the advanced courses J. S. Milne taught between 1986 and 1999.
  Elliptic Curves Handout http://www.maths.warwick.ac.uk/~miles/MA426/
Syllabus and detailed reading list by Miles Reid, University of Warwick.
  Elliptic Divisibility Sequences http://www.mth.uea.ac.uk/~h090/EDS.html
Articles and links, compiled by Graham Everest.
  History of Elliptic Curve Rank Records http://www.math.hr/~duje/tors/rankhist.html
A table up to rank 24 compiled by Andrej Dujella.
  Elliptical Curve Cryptography http://www.cryptoman.com/elliptic.htm
Explains the difference between an elliptical curve and an ellipse. Discusses fields, applications, choosing a fixed point, and related topics.
  14H52: Elliptic Curves http://www.math.niu.edu/~rusin/known-math/index/14H52.html
From the Known Math series.
  Arithmetic of Cuves http://math.scu.edu/~eschaefe/nt.html
Papers and surveys by Ed Schaefer.
  Elliptic Curves and Elliptic Functions http://cgd.best.vwh.net/home/flt/flt03.htm
Introductory notes by Charles Daney.
  On 5 and 7 Descents for Elliptic Curves http://www.dpmms.cam.ac.uk/~taf1000/thesis.html
Tom Fisher's Ph.D. thesis (Cambridge, 2000) in DVI and PS format.
  Elliptic Curves and Formal Groups http://www.ma.utexas.edu/users/voloch/lst.html
Lecture notes from a seminar J. Lubin, J.-P. Serre and J. Tate.
  Elliptic Curves with H. A. Verrill http://www.math.lsu.edu/~verrill/teaching/math7280/index.html
Lecture notes and resources by Helena Verrill, Louisiana State University, 2004.
  Papers by Richard Borcherds http://math.berkeley.edu/~reb/papers/
Including proof of the Moonshine Conjecture (TeX,DVI,PDF).
  Elliptic Curves and Right Triangles http://math.stanford.edu/~rubin/lectures/sumo/
Slides (GIF) of lectures by Karl Rubin at Stanford University.
  Kolyvagin Seminar http://math.berkeley.edu/~osserman/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 http://tom.womack.net/maths/maths.htm
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.
  Prime Values of Elliptic Divisibility Sequences http://www.mth.uea.ac.uk/~h090/primeEDS.html
By Graham Everest.
  Modular Forms and Hecke Operators http://modular.fas.harvard.edu/MF.html
Notes by William A. Stein of a course by Ken Ribet.
  Elliptic Functions and Elliptic Curves http://www.math.jussieu.fr/~nekovar/co/ln/el/
Lecture notes by Jan Neková (PS/PDF).
  Iwasawa Theory of Elliptic Curves http://www.math.washington.edu/~greenber/research.html
Lecture notes and surveys by Ralph Greenberg, University of Washington (PS).
  Modular Forms Course http://modular.fas.harvard.edu/Tables/Notes/
Notes of a 1996 Berkeley course of Ken Ribet's on modular forms and Hecke operators.
  A Proof of the Full Shimura-Taniyama-Weil Conjecture http://www.ams.org/notices/199911/comm-darmon.pdf
Article by Henri Darmon on the completion of the proof by Wiles, Breuil, Conrad, Diamond and Taylor.
  Rational Points on Elliptic Curves http://www.math.rutgers.edu/~tunnell/math574.html
A course by Jerrold Tunnell. An introduction to rational points on elliptic curves through examples.
  Explicit Approaches to Modular Abelian Varieties http://modular.fas.harvard.edu/papers/explicit/
William Stein, Ph.D. thesis, Berkeley, 2000.
  Elliptic Curves II http://home.imf.au.dk/matjph/Ell-E99.html
Lecture notes by Johan P. Hansen.
  Counting Points on Elliptic Curves http://www.math.jussieu.fr/~fouquet/elliptic.html
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.
  Elliptic Curves and Their Applications to Cryptography http://www.lix.polytechnique.fr/Labo/Andreas.Enge/buch/buch/buch.html
Web text by Andreas Enge.
  Recent Progress in the Theory of Elliptic Curves http://www.cms.math.ca/CMS/Events/winter98/w98-abs/node2.html
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.
  Torsion Points on Elliptic Curves http://mat.uab.cat/~xarles/elliptic.html
Elementary introduction and brief explanation of some well-known results.

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