Elliptic Curves and Modular Forms

Arithmetic of Cuves
Papers and surveys by Ed Schaefer.
http://math.scu.edu/~eschaefe/nt.html

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

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/Birch_and_Swinnerton-Dyer_Conjecture/

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.
http://www.math.jussieu.fr/~fouquet/elliptic.html

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/

ECDL Project
Elliptic Curve Discrete Logarithms Project. They solved ECC2K-108 in April 2000. History and related papers.
http://pauillac.inria.fr/~harley/ecdl/

ECMNET
The ECMNET Project to find large factors by the Elliptic Curve Method, mainly Cunningham numbers.
http://www.loria.fr/~zimmerma/records/ecmnet.html

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

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

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

Elliptic Curves and Elliptic Functions
Introductory notes by Charles Daney.
http://cgd.best.vwh.net/home/flt/flt03.htm

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

Elliptic Curves and Right Triangles
Slides (GIF) of lectures by Karl Rubin at Stanford University.
http://math.stanford.edu/~rubin/lectures/sumo/

Elliptic Curves and Their Applications to Cryptography
Web text by Andreas Enge.
http://www.lix.polytechnique.fr/Labo/Andreas.Enge/buch/buch/buch.html

Elliptic Curves Handout
Syllabus and detailed reading list by Miles Reid, University of Warwick.
http://www.maths.warwick.ac.uk/~miles/MA426/

Elliptic Curves II
Lecture notes by Johan P. Hansen.
http://home.imf.au.dk/matjph/Ell-E99.html

Elliptic Curves with H. A. Verrill
Lecture notes and resources by Helena Verrill, Louisiana State University, 2004.
http://www.math.lsu.edu/~verrill/teaching/math7280/index.html

Elliptic Divisibility Sequences
Articles and links, compiled by Graham Everest.
http://www.mth.uea.ac.uk/~h090/EDS.html

Elliptic Functions and Elliptic Curves
Lecture notes by Jan Nekovář (PS/PDF).
http://www.math.jussieu.fr/~nekovar/co/ln/el/

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

Explicit Approaches to Modular Abelian Varieties
William Stein, Ph.D. thesis, Berkeley, 2000.
http://modular.fas.harvard.edu/papers/explicit/

14H52: Elliptic Curves
From the Known Math series.
http://www.math.niu.edu/~rusin/known-math/index/14H52.html

History of Elliptic Curve Rank Records
A table up to rank 24 compiled by Andrej Dujella.
http://www.math.hr/~duje/tors/rankhist.html

Iwasawa Theory of Elliptic Curves
Lecture notes and surveys by Ralph Greenberg, University of Washington (PS).
http://www.math.washington.edu/~greenber/research.html

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/

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://math.berkeley.edu/~osserman/seminar/

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

Modular Forms and Hecke Operators
Notes by William A. Stein of a course by Ken Ribet.
http://modular.fas.harvard.edu/MF.html

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/

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

Papers by Richard Borcherds
Including proof of the Moonshine Conjecture (TeX,DVI,PDF).
http://math.berkeley.edu/~reb/papers/

Prime Values of Elliptic Divisibility Sequences
By Graham Everest.
http://www.mth.uea.ac.uk/~h090/primeEDS.html

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]
http://www.ams.org/notices/199911/comm-darmon.pdf

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

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

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/

Torsion Points on Elliptic Curves
Elementary introduction and brief explanation of some well-known results.
http://mat.uab.cat/~xarles/elliptic.html