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This page is a collection of links on research articles on elliptic curves and related topics (applications, modular forms, FLT).

• Introduction.
  • Introduction élémentaire à la théorie des courbes elliptiques (Marc Joye).
  • Draft chapters 1,2 of elliptic curve handbook ECH1. (Ian Connell).
  • The Elliptic Curves Virtual Study Group.
  • Arithmetic of elliptic curves with complex multiplication (lecture notes by Karl Rubin).
  • Various lecture notes by James Milne.
• Algorithmic and cryptographic applications.
  • George Barwood's elliptic curve cryptography FAQ.
  • Elliptic Curves and Primality Proving. (Atkin & Morain).
  • Finding suitable curves for the Elliptic Curve factoring method. (Atkin & Morain).
  • Factorization of large integers on some vector and parallel computers. (Craig Eldershaw and Richard P. Brent).
  • François Morain's articles.
  • John Cremona's recent papers, preprints and talks.
  • Elliptic Curve Cryptosystems (ECC) Questions & Answers, (Certicom).
  • Counting points on elliptic curves over finite fields, René SCHOOF.
  • Schoof 's algorithm and isogeny cycles, Jean-Marc Couveignes et François Morain.
  • Computing l-isogenies with the p-torsion, Jean-Marc Couveignes.
  • Calcul du nombre de points sur une courbe elliptique dans un corps fini : aspects algorithmiques, François MORAIN.
  • Polynomials with integral coefficients, equivalent to a given polynomial, Janos KOLLAR.
  • Classical Invariants and Elliptic Curves, John Cremona.
• Modular forms aspects.
  • Modularity of a family of elliptic curves, by Fred Diamond, Kenneth Kramer
  • Galois representations and modular forms, by Kenneth A. Ribet.
  • A refinement of the Faltings-Serre method, by Nigel Boston.
  • Modularity of a family of elliptic curves, by Fred Diamond, Kenneth Kramer.
  • Classical and overconvergent modular forms, Robert F. Coleman.
  • Some propreties of Hecke operators.
  • Elliptic modular units.
  • Stark-Heegner points over real quadratic fields, H.Darmon.
  • Computing Periods of Cusp Forms and modular elliptic curves, John Cremona.
  • Modular Symbols and the computation of Modular Elliptic Curves, John Cremona.
  • Computing the Degree of the Modular Parametrization of a Modular Elliptic Curve, John Cremona.
  • On the conjecture of Birch and Swinnerton-Dyer for elliptic curves, by Cristian D. Gonzalez-Aviles.
  • Elliptic curves, p-adic modular forms and Atkin's operator U_p, by Andy Baker (+ other papers).
  • Notes from K. Ribet's lectures on Galois representations, modular forms, Hecke algebras, modular curves...
• L-functions.
  • Zéros des fonctions L des courbes elliptiques, by S. Fermigier.
  • Étude expérimentale du rang de familles de courbes elliptiques sur Q, by S. Fermigier.
  • Fonctions L p-adiques d'une courbe elliptique, d'après B. Perrin-Riou, M. Savin.
  • Eléments explicites dans $K_2$ d'une courbe elliptique, Klaus Rolshausen.
• Rank of elliptic curves.
  • Courbes elliptiques de rang >=11 sur Q(t), by J.-F. Mestre.
  • Courbes elliptiques de rang >=12 sur Q(t), by J.-F. Mestre.
  • Un exemple de courbe elliptique sur Q de rang >=15, by J.-F. Mestre.
  • Rang de courbes elliptiques d'invariant donné, J.-F. Mestre.
  • Rang de courbes elliptiques d'invariant nul, J.-F. Mestre.
  • Exemples de courbes elliptiques de grand rang sur Q(t) et sur Q possédant des points de 2-torsion, by S. Fermigier.
  • Construction de courbes elliptiques de grand rang sur Q(t) et sur Q possédant des points de 2-torsion, by S. Fermigier.
  • Construction of high-rank elliptic curves over Q and Q(t) with non-trivial 2-torsion (extended abstract), by S. Fermigier.
  • An elliptic curve over Q of rank >=22, by S. Fermigier.
  • On the rank of an elliptic surface, J. Silverman.
  • The average rank of an algebraic family of elliptic curves, J. Silverman.
  • A bound for the Mordell-Weil rank of an elliptic surface after a cylic base extension, J. Silverman.
  • An elliptic surface of Mordell-Weil rank 8 over the rational numbers, Charles F. Schwartz.
  • Computing the rank of elliptic curves over real quadratic fields of class number 1, John Cremona.
  • Classical Invariants and 2-descent on Elliptic Curves, John Cremona.
  • Higher Descents on Elliptic Curves, John Cremona.
• Heights.
  • The elliptic Mahler measure. (G. Everest & Brid ni Fhlathuin).
  • Computing rational points on rank 1 elliptic curves via L-series and canonical heights, J. Silverman.
  • Bounds for the canonical height and integral points on elliptic curves over function fields, Amilcar Pacheco.
  • On Serre's equation: X^4 + Y^4 = 17Z^4, S. SIKSEK.
  • Bounding the elliptic Mahler measure II, Graham Everest.
• Torsion.
  • Bornes effectives pour la torsion des courbes elliptiques sur les corps des nombres, by Pierre Parent.
  • Rational torsion of prime order in elliptic curves over number fields, by Sheldon Kamienny and Barry Mazur.
• Jacobians.
  • Jacobiennes de certaines courbes de genre 2 : torsion et simplicite, Franck LEPREVOST.
• Bibliographies.
  • ``Some interesting references on elliptic curves...'' (Marc Joye).
  • A list of documents on Fermat's Last Theorem, (incl. articles from Ribet, Mazur, Adler, Rubin, Silverberg...).
  • Arithmetic Geometry: What is it and what is it good for? Bibliography
• Others or unsorted (yet).
  • Uniformity of stably integral points on elliptic curves by Dan Abramovich.
  • Polylogarithmic Extensions on Mixed Shimura varieties. Part III The elliptic polylogarithm, by Joerg Wildeshaus.
  • Elliptic Curves, by csjutla@watson.ibm.com.
  • Papers by Andrew Granville.
  • Beppo Levi and the arithmetic of elliptic curves, by Norbert Schappacher.
  • Algebraic Number Theory Archives.
  • Joseph Silverman's home page.
  • ``Chapitre 2. Sur la distance d'un point algebrique a l'origine dans les varietes abeliennes''.
  • Brauer groups of local elliptic and hyperelliptic curves and central division algebras over their function fields, Vyacheslav Yanchevskii and Gennady Margolin.
  • On an elliptic analogue of Zagier's conjecture, Jörg Wildeshaus.
  • Triangular numbers and elliptic curves, Jasbir S. Chahal and Jaap Top.
  • ON THE EQUATION a^p + 2^alpha b^p + c^p = 0, Kenneth A. Ribet.
  • On Bloch-Kato conjecture of Tamagawa numbers for Hecke characters of imaginary quadratic number field, Bing Han.

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Stéfane Fermigier. Page created (or updated) on Sat Dec 5 12:20:21 1998.

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