Elliptic Curves

Level I

• Reza Akhtar An Introduction to Elliptic Curves
• George Barwood Elliptic curve cryptography FAQ
• Ezra Brown
  1. Three Fermat Trails to Elliptic Curves
  2. Magic Squares, Finite Planes and Points of Inflection on Elliptic Curves
  3. Elliptic Curves from Mordell to Diophantus and back
• Charles Daney Elliptic Curves and Elliptic Functions
• Ed Eikenberg Congruent Numbers and Elliptic Curves
• Marc Joye, introduction elementaire (Fr)
• Math circle Berkeley, Elliptic Curves
• Pamela Peters Groups Formed by Rational Points on Elliptic Curves
• Bjorn Poonen Elliptic curves
• Alf van der Poorten
  1. Fermat's Last Theorem
  2. Remarks on Fermat's Last Theorem
• Jim Propp Fermat's Last Theorem and the Fourth Dimension
• Harold Reiter Pythagorean Triples, the Unit Circle, and Fermat's Last Theorem
• Lee J. Stemkoski Introduction to Elliptic Curves
• Henk C.A. van Tilborg Elliptic Curves
• Helena Verrill, Group Law for elliptic curves
• Mike Woodbury Finite Groups on Elliptic Curves
• Xavier Xarles torsion points (pdf)
• Takayuki Yato Study on elliptic and hyperelliptic curve for integer factorization
• Eric von York, Elliptic curves over finite fields

Level II

• Jeff Achter On Computing the Rank of Elliptic Curves
• Hege R. Frium The Group Law on Elliptic Curves on Hesse form
• Jerome W. Hoffman Topics in Elliptic Curves and Modular Forms
• Dimitar Jetchev Visibility of the Tate-Shafarevich group; Principal Homogenous Spaces, Selmer Groups, and Shafarevich-Tate Groups
• Barry Mazur, Three lectures about the arithmetic of elliptic curves
• Joshua Plotkin, The Mordell-Weil Theorem
• Alvaro Lozano Robledo Finding points on elliptic curves: Very explicit methods
• Ed Schaefer, Mordell-Weil rank and Selmer groups
• Jonathan Touboul, Joseph Ribeau, Théorème de Hasse
• Helena Verrill Monstrous Moonshine and Mirror Symmetry
• Eric von York Elliptic Curves Over Finite Fields

Modular Curves

• Noam Elkies The Klein quartic
• Seth Kleinerman On the torsion points of elliptic curves and modular abelian varieties
• Alexei Pantchichkine, Formes modulaires
• Tom Weston The modular curves X₀(11) and X₁(11)

Selmer and Tate-Shafarevich Groups

• A. C. Cojocaru, W. Duke, Reductions of an Elliptic Curve and their Tate-Shafarevich Groups
• Z. Djabri, Edward Schaefer, Nigel Smart, Computing the p-Selmer Group of an Elliptic Curve
• Hendrik Kasten, A Stickelberger Index for the Tate-Shafarevich Group
• Remke Kloosterman The p-part of Tate-Shafarevich groups of elliptic curves can be arbitrarily large
• Remke Kloosterman Large Selmer groups
• Remke Kloosterman Lectures on Selmer groups
• Abderrahmane Nitaj Invariants des courbes de Frey-Hellegouarch et grands groupes de Tate-Shafarevich
• Ken Ono, Tate-Shafarevich groups of the congruent number elliptic curves
• Harvey Rose, On Some Elliptic Curves with Large Sha
• K. Rubin, A. Silverberg, Ranks of elliptic curves
• Alice Silverberg Elliptic Curves: The State of the Art What Number Theorists Want