Computing integral points on elliptic curves
J. Gebel ; A. Pethő ; H. G. Zimmer
Acta Arithmetica, Tome 68 (1994), p. 171-192 / Harvested from The Polish Digital Mathematics Library
Publié le : 1994-01-01
EUDML-ID : urn:eudml:doc:206653
@article{bwmeta1.element.bwnjournal-article-aav68i2p171bwm,
     author = {J. Gebel and A. Peth\H o and H. G. Zimmer},
     title = {Computing integral points on elliptic curves},
     journal = {Acta Arithmetica},
     volume = {68},
     year = {1994},
     pages = {171-192},
     zbl = {0816.11019},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-aav68i2p171bwm}
}
J. Gebel; A. Pethő; H. G. Zimmer. Computing integral points on elliptic curves. Acta Arithmetica, Tome 68 (1994) pp. 171-192. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav68i2p171bwm/

[000] [B] A. Baker, The Diophantine equation y²=ax³+bx²+cx+d, J. London Math. Soc. 43 (1968), 1-9.

[001] [D] S. David, Minorations de formes linéaires de logarithmes elliptiques, manuscript, Paris, 1993.

[002] [F] G. Frey, L-series of elliptic curves: results, conjectures and consequences, in: Proc. Ramanujan Centenn. Internat. Conf., Annamalainagar, December 1987, 31-43.

[003] [GPP] I. Gaàl, A. Pethő and M. Pohst, On the resolution of index form equations in biquadratic number fields II, J. Number Theory 38 (1991), 35-51. | Zbl 0726.11023

[004] [GSch] I. Gaàl and N. Schulte, Computing all power integral bases of cubic number fields II, Math. Comp. 53 (1989), 689-696. | Zbl 0677.10013

[005] [G] F. R. Gantmacher, The Theory of Matrices I, Chelsea, New York, N.Y., 1977.

[006] [GZ] J. Gebel and H. G. Zimmer, Computing the Mordell-Weil group of an elliptic curve over ℚ, in: Elliptic Curves and Related Topics, H. Kisilevsky and M. Ram Murty (eds.), CRM Proceedings and Lecture Notes, Amer. Math. Soc., Providence, RI, 1994, 61-83. | Zbl 0809.14024

[007] [Gr] D. R. Grayson, The arithmetic-geometric mean, Arch. Math. (Basel) 52 (1989), 507-512. | Zbl 0686.14040

[008] [HSi] A. Hindry and J. H. Silverman, The canonical height and integral points on elliptic curves, Invent. Math. 93 (1988), 419-450. | Zbl 0657.14018

[009] [L1] S. Lang, Diophantine approximation on toruses, Amer. J. Math. 86 (1964), 521-533. | Zbl 0142.29601

[010] [L2] S. Lang, Elliptic Functions, Addison-Wesley, Reading, 1973.

[011] [L3] S. Lang, Elliptic Curves; Diophantine Analysis, Grundlehren Math. Wiss. 231, Springer, Berlin, 1978.

[012] [L4] S. Lang, Conjectured diophantine estimates on elliptic curves, in: Progr. Math. 35, Birkhäuser, Basel, 1983, 155-171.

[013] [LLL] A. K. Lenstra, H. W. Lenstra and L. Lovász, Factoring polynomials with rational coefficients, Math. Ann. 261 (1982), 515-534. | Zbl 0488.12001

[014] [M] Yu. I. Manin, Cyclotomic fields and modular curves, Russian Math. Surveys 26 (6) (1971), 7-78. | Zbl 0266.14012

[015] [Mz] B. Mazur, Rational points on modular curves, in: Modular Functions of One Variable V, Lecture Notes in Math. 601, Springer, Berlin, 1977, 107-148.

[016] [Me] J.-F. Mestre, Formules explicites et minorations de conducteurs de variétés algébriques, Compositio Math. 58 (1986), 209-232.

[017] [PS] A. Pethő und R. Schulenberg, Effektives Lösen von Thue Gleichungen, Publ. Math. Debrecen 34 (1987), 189-196.

[018] [PdW] A. Pethő and B. M. M. de Weger, Product of prime powers in binary recurrence sequences, Part I: The hyperbolic case, with an application to the generalized Ramanujan-Nagell equation, Math. Comp. 47 (1986), 713-727. | Zbl 0623.10011

[019] [Sch] W. Schmidt, Integer points on curves of genus 1, Compositio Math. 81 (1992), 33-59. | Zbl 0747.11026

[020] [S] C. L. Siegel, Über einige Anwendungen diophantischer Approximationen, Abh. Preuss. Akad. Wiss. (1929), 1-41. | Zbl 56.0180.05

[021] [Si1] J. H. Silverman, A quantitative version of Siegel's theorem, J. Reine Angew. Math. 378 (1981), 60-100.

[022] [Si2] J. H. Silverman, The difference between the Weil height and the canonical height on elliptic curves, Math. Comp. 55 (1990), 723-743. | Zbl 0729.14026

[023] [SM] SIMATH, Manual, Saarbrücken, 1993.

[024] [St] R. P. Steiner, On Mordell's equation y²-k = x³. A problem of Stolarsky, Math. Comp. 46 (1986), 703-714. | Zbl 0601.10011

[025] [ST] R. J. Stroeker and N. Tzanakis, Solving elliptic diophantine equations by estimating linear forms in elliptic logarithms, Acta Arith. 67 (1994), 177-196. | Zbl 0805.11026

[026] [TdW1] N. Tzanakis and B. M. M. de Weger, On the practical solution of the Thue equation, J. Number Theory 31 (1989), 99-132. | Zbl 0657.10014

[027] [TdW2] N. Tzanakis and B. M. M. de Weger, How to explicitly solve a Thue-Mahler equation, Compositio Math. 84 (1992), 223-288. | Zbl 0773.11023

[028] [dW] B. M. M. de Weger, Algorithms for diophantine equations, Ph.D. Thesis, Centrum voor Wiskunde en Informatica, Amsterdam, 1987. | Zbl 0625.10013

[029] [Za] D. Zagier, Large integral points on elliptic curves, Math. Comp. 48 (1987), 425-436. | Zbl 0611.10008

[030] [Zs] H. Zassenhaus, On Hensel factorization, I, J. Number Theory 1 (1969), 291-311.

[031] [Zi1] H. G. Zimmer, On the difference between the Weil height and the Néron-Tate height, Math. Z. 147 (1976), 35-51. | Zbl 0303.14003

[032] [Zi2] H. G. Zimmer, On Manin's conditional algorithm, Bull. Soc. Math. France Mém. 49-50 (1977), 211-224.

[033] [Zi3] H. G. Zimmer, Generalization of Manin's conditional algorithm, in: SYMSAC 76, Proc. ACM Sympos. Symbolic Alg. Comp., Yorktown Heights, N.Y., 1976, 285-299.

[034] [Zi4] H. G. Zimmer, Computational aspects of the theory of elliptic curves, in: Number Theory and Applications, R. A. Mollin (ed.), Kluwer, 1989, 279-324.

[035] [Zi5] H. G. Zimmer, A limit formula for the canonical height of an elliptic curve and its application to height computations, in: Number Theory, R. A. Mollin (ed.), W. de Gruyter, Berlin, 1990, 641-659. | Zbl 0738.14020