the entire directory only in Number_Theory/Elliptic_Curves_and_Modular_Forms

See also:

• Science: Math: Number Theory: Diophantine Equations: Fermat's Last Theorem (13)
• Science: Math: Number Theory: Factoring (40)
• Science: Math: Number Theory: Prime Numbers: Primality Tests: Primality Proving (11)

• 14H52: Elliptic Curves - From the Known Math series.
• 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]
• Algorithms for Modular Elliptic Curves - Book by John Cremona, with introduction, tables and software.
• An Elementary Introduction to Elliptic Curves - By Len Charlap, David Robbins and Raymond Coley. Downloadable text in PostScript (.ps) format.
• Arithmetic of Cuves - Papers and surveys by Ed Schaefer.
• Bibliography for Automorphic and Modular Forms, L-Functions, Representations, and Number Theory - Compiled by Paul Garrett, 1996.
• 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.
• Course Notes - Full notes as .dvi, .pdf, and .ps files for all the advanced courses J. S. Milne taught between 1986 and 1999.
• ECDL Project - Elliptic Curve Discrete Logarithms Project. They solved ECC2K-108 in April 2000. History and related papers.
• ECMNET - The ECMNET Project to find large factors by the Elliptic Curve Method, mainly Cunningham numbers.
• Elliptic Curves Handout - Syllabus and detailed reading list by Miles Reid, University of Warwick.
• Elliptic Curves II - Lecture notes by Johan P. Hansen.
• Elliptic Curves and Formal Groups - Lecture notes from a seminar J. Lubin, J.-P. Serre and J. Tate.
• Elliptic Curves with H. A. Verrill - Lecture notes and resources by Helena Verrill, Louisiana State University, 2004.
• Elliptic Divisibility Sequences - Articles and links, compiled by Graham Everest.
• Elliptic Functions and Elliptic Curves - Lecture notes by Jan Nekovář (PS/PDF).
• Elliptical Curve Cryptography - Explains the difference between an elliptical curve and an ellipse. Discusses fields, applications, choosing a fixed point, and related topics.
• History of Elliptic Curve Rank Records - A table up to rank 24 compiled by Andrej Dujella.
• Iwasawa Theory of Elliptic Curves - Lecture notes and surveys by Ralph Greenberg, University of Washington (PS).
• Joseph Silverman - Includes errata for his books Rational Points on Elliptic Curves and Advanced Topics in the Arithmetic of Elliptic Curves.
• 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.
• 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.
• Modular Forms Example Sheets - From a course on modular forms.
• On 5 and 7 Descents for Elliptic Curves - Tom Fisher's Ph.D. thesis (Cambridge, 2000) in DVI and PS format.
• Papers by Richard Borcherds - Including proof of the Moonshine Conjecture (TeX,DVI,PDF).
• Prime Values of Elliptic Divisibility Sequences - By Graham Everest.
• Rational Points on Elliptic Curves - A course by Jerrold Tunnell. An introduction to rational points on elliptic curves through examples.
• 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.
• Richard Taylor - Publications including the joint paper with Andrew Wiles which completed the proof of Fermat's Last Theorem.
• 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].
• Torsion Points on Elliptic Curves - Elementary introduction and brief explanation of some well-known results.

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