Détermination de courbes elliptiques pour la conjecture de Szpiro

Abderrahmane Nitaj

Acta Arithmetica (1998)

  • Volume: 85, Issue: 4, page 351-376
  • ISSN: 0065-1036

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Abderrahmane Nitaj. "Détermination de courbes elliptiques pour la conjecture de Szpiro." Acta Arithmetica 85.4 (1998): 351-376. <http://eudml.org/doc/207174>.

@article{AbderrahmaneNitaj1998,
author = {Abderrahmane Nitaj},
journal = {Acta Arithmetica},
keywords = {courbe elliptique; isogénie; conjecture de Szpiro; elliptic curves; isogenies; Szpiro's conjecture; Szpiro's quotient; diophantine equations},
language = {fre},
number = {4},
pages = {351-376},
title = {Détermination de courbes elliptiques pour la conjecture de Szpiro},
url = {http://eudml.org/doc/207174},
volume = {85},
year = {1998},
}

TY - JOUR
AU - Abderrahmane Nitaj
TI - Détermination de courbes elliptiques pour la conjecture de Szpiro
JO - Acta Arithmetica
PY - 1998
VL - 85
IS - 4
SP - 351
EP - 376
LA - fre
KW - courbe elliptique; isogénie; conjecture de Szpiro; elliptic curves; isogenies; Szpiro's conjecture; Szpiro's quotient; diophantine equations
UR - http://eudml.org/doc/207174
ER -

References

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  1. [1] M. Ayad, Points S-entiers des courbes elliptiques, Manuscripta Math. 76 (1992), 305-324. Zbl0773.14014
  2. [2] C. Batut, D. Bernardi, H. Cohen and M. Olivier, PARI-GP, a computer system for number theory, Version 1.39, ftp://megrez.ceremab.u-bordeaux.fr/~pub/pari/. 
  3. [3] H. Cohen, A Course in Computational Algebraic Number Theory, Grad. Texts in Math. 138, Springer, Berlin, 1993. 
  4. [4] I. Connell, APECS, Version 3.7, 1996, ftp://math.mcgill.ca/pub/apecs/. 
  5. [5] J. Cremona, Algorithms for Modular Elliptic Curves, Cambridge University Press, Cambridge, 1992. Zbl0758.14042
  6. [6] E. Fouvry, M. Nair et G. Tenenbaum, L'ensemble exceptionnel dans la conjecture de Szpiro, Bull. Soc. Math. France 120 (1992), 485-506. Zbl0770.11030
  7. [7] M. Hindry and J. H. Silverman, The canonical height and integral points on elliptic curves, Invent. Math. 93 (1988), 419-450. Zbl0657.14018
  8. [8] D. Husemoller, Elliptic Curves, Grad. Texts in Math. 111, Springer, Berlin, 1986. 
  9. [9] D. S. Kubert, Universal bounds on the torsion of elliptic curves, Proc. London Math. Soc. 33 (1976), 193-237. Zbl0331.14010
  10. [10] T. Nagell, Recherches sur l'arithmétique des cubiques planes du premier genre dans un domaine de rationalité quelconque, Nova Acta Soc. Sci. Upsal, Ser. IV 15, 6 (1952), 1-66. Zbl0048.27102
  11. [11] A. Nitaj, Algorithms for finding good examples for the abc and Szpiro conjectures, Experiment. Math. 3 (1993), 223-230. Zbl0818.11050
  12. [12] A. Nitaj, Tables of good abc-examples, preprint, Saarbrücken, 1997. 
  13. [13] J. Oesterlé, Nouvelles approches du 'théorème' de Fermat, Séminaire Bourbaki 1987-88, no. 694, Astérisque 161-162 (1988), 165-186. 
  14. [14] J. H. Silverman, The Arithmetic of Elliptic Curves, Grad. Texts in Math. 106, Springer, Berlin, 1986. 
  15. [15] SIMATH, a computer algebra system, Version 3.10.3, Simath-Gruppe, Saarbrücken, 1996, ftp://ftp.math.uni-sb.de:/pub/simath. 
  16. [16] L. Szpiro, Propriétés numériques du faisceau dualisant relatif, dans : Pinceaux de Courbes de Genre au Moins Deux, Astérisque 86 (1981), 44-78. 
  17. [17] L. Szpiro, Discriminant et conducteur, dans : Séminaire sur les Pinceaux de Courbes Elliptiques, Astérisque 183 (1990), 7-17. 
  18. [18] H. M. Tschöpe and H. G. Zimmer, Computation of the Néron-Tate height on elliptic curves, Math. Comp. 48 (1987), 351-370. Zbl0611.14028
  19. [19] J. Vélu, Isogénies entre courbes elliptiques, C. R. Acad. Sci. Paris Sér. I Math. 273 (1971), 238-241. Zbl0225.14014
  20. [20] B. M. M. de Weger, A + B = C and big III's, Quart. J. Math. Oxford Ser. (2) 49 (1998), 105-128. 

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