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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 role in the recent resolution of the conjecture known as Fermat's Last Theorem.

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Rational Points on Elliptic Curves A course by Jerrold Tunnell. An introduction to rational points on elliptic curves through examples. www.math.rutgers.edu/~tunnell/math574.html

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

Joseph Silverman Includes errata for his books Rational Points on Elliptic Curves and Advanced Topics in the Arithmetic of Elliptic Curves. www.math.brown.edu/~jhs

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

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

Elliptic Curves and Formal Groups Lecture notes from a seminar J. Lubin, J.-P. Serre and J. Tate. www.ma.utexas.edu/users/voloch/lst.html

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

Elliptic Curves and Cryptology Marc Joye's list of elliptic curve resources includes people, books, and links. Many preprints are available from the site. www.geocities.com/marcjoye/biblio_ell.html

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. tom.womack.net/maths/maths.htm

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

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

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

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

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

Algorithms for Modular Elliptic Curves Book by John Cremona, with introduction, tables and software. www.maths.nott.ac.uk/personal/jec/book/chapter1.html

Modular Forms Example Sheets From a course on modular forms. math.berkeley.edu/~reb/modularforms

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. www.ams.org/notices/199911/comm-darmon.pdf

Monstrous Moonshine the surprising and mysterious connections between the monster (and also other finite sporadic simple groups) and modular functions. cicma.concordia.ca/faculty/cummins/moonshine.html

Modularity of Elliptic Curves and Beyond Workshop, MSRI Berkeley, 6-10 December 1999. www.msri.org/activities/events/9900/hottopics

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. www.cms.math.ca/CMS/Events/winter98/w98-abs/node2.html

Bibliography for Automorphic and Modular Forms, L-Functions, Representations, and Number Theory Compiled by Paul Garrett, 1996. www.math.umn.edu/~garrett/m/b/bib.html

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

Modular Forms Course Notes of a 1996 Berkeley course of Ken Ribet's on modular forms and Hecke operators. modular.fas.harvard.edu/Tables/Notes

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

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

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