Courbes elliptiques

Cette page est une collection de liens sur des articles sur les courbes elliptiques et leurs aplications.

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 (notes de cours de Karl Rubin).
- Various lecture notes by James Milne.
Aspects et applications algorithmiques/cryptographiques.
- 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).
- Les articles de François Morain.
- 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.
Lien avec les formes modulaires.
- 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...
Fonctions L.
- 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.
Rang des courbes elliptiques.
- 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.
Hauteurs.
- 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.
Jacobiennes.
- Jacobiennes de certaines courbes de genre 2 : torsion et simplicite, Franck LEPREVOST.
Références.
- ``Some interesting references on elliptic curves...'' (Marc Joye).
- Une liste de documents sur le th. de Fermat, (avec des articles de Ribet, Mazur, Adler, Rubin, Silverberg...).
- Arithmetic Geometry: What is it and what is it good for? Bibliography
Divers ou non-classés.
- 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 créée (ou mise à jour) le Sat Dec 5 12:20:23 1998.