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Elliptic Curves and Modular Forms

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

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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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