In this page we collect links, articles, and other resources pertaining to elliptic curves. If you want to fix or suggest a link, please send me a message to alvaro.lozano-robledo@uconn.edu. Thanks!
- Wikipedia entry on elliptic curves.
- Cremona’s Database and the LMFDB database
- Sage Math, and Magma.
Books
- Neil I. Koblitz, “Introduction to Elliptic Curves and Modular Forms“, Graduate Texts in Mathematics (Book 97), Springer; 2nd edition (April 29, 1993).
- (My own) Alvaro Lozano-Robledo, “Elliptic Curves, Modular Forms, and their L-Functions“, American Mathematical Society (February 8, 2011).
- J. S. Milne, “Elliptic Curves“, Kea Books, 2006. (Free at the author’s website)
- Joseph H. Silverman, “The Arithmetic of Elliptic Curves“, Springer; 2nd ed. 2009 edition (March 25, 2016).
- Joseph H. Silverman and John Tate, “Rational Points on Elliptic Curves“, Springer; 2nd ed. 2015 edition.
- L. C. Washington, “Elliptic Curves: Number Theory and Cryptography“, Second Edition (Discrete Mathematics and Its Applications), Chapman & Hall/CRC (April 3, 2008).
About the Rank
- Andrej Dujella‘s site on
- High rank elliptic curves with prescribed torsion (notice the long list of references at the bottom of that page!).
- History of elliptic curves rank records
- Noam Elkies‘ pages:
- Noam Elkies, “Three lectures on elliptic surfaces and curves of high rank“.
- Noam D. Elkies, Nicholas F. Rogers, “Elliptic Curves x^3 + y^3 = k of High Rank“.
- Noam Elkies and Mark Watkins, “Elliptic curves of large rank and small conductor“.
- Karl Rubin and Alice Silverberg, “Ranks of elliptic curves“, Bull. of the Am. Math. Soc., Volume 39, Number 4, Pages 455–474.
- Tom Womack‘s page on