Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-26T11:27:05.944Z Has data issue: false hasContentIssue false
  • English
  • Français

S-integral points on elliptic curves

Published online by Cambridge University Press:  24 October 2008

N. P. Smart
N. P. Smart
Affiliation:
Department of Computing Mathematics, University of Wales College of Cardiff, Cardiff CF2 4YN, Wales.
Get access Rights & Permissions [Opens in a new window]

Extract

In this paper I give an algorithm to find all ‘small’ S-integral points on an elliptic curve. I would like to thank N. Stephens for suggesting I consider such equations and the Wingate Foundation for supporting me whilst carrying out the research. As is usual c1, c2, …, will denote positive real constants which are effectively computable.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 116 , Issue 3 , November 1994 , pp. 391 - 399
Copyright
Copyright © Cambridge Philosophical Society 1994

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Ayad, M.. Points Δ-entiers sur les courbes elliptiques. J. Number Theory 38 (1991), 323–337.CrossRefGoogle Scholar
[2]Cremona, J. E.. Algorithms For Modular Elliptic Curves (Cambridge University Press, 1993).Google Scholar
[3]David, S.. Minorations de formes linéaires de logarithmes elliptiques. Publ. Math. de l'Univ. Pierre et Marie Curie, 106, Problèmes diophantiens 1991–1992, exposé no 3.Google Scholar
[4]Lang, S.. Elliptic Curves: Diophantine Analysis (Springer-Verlag, 1978).CrossRefGoogle Scholar
[5]Lenstra, A. K., Lenstra, H. W. and Lovász, L.. Factoring polynomials with rational coefficients. Math. Ann. 261 (1982), 515–534.CrossRefGoogle Scholar
[6]Silverman, J. H.. The Arithmetic Of Elliptic Curves (Springer-Verlag, 1986).CrossRefGoogle Scholar
[7]Stroeker, R. J. and Tzanakis, N.. Solving elliptic diophantine equations by estimating linear forms in elliptic logarithms, to appear in Acta. Arith.Google Scholar
[8]Tzanakis, N. and De Weger, B. M. M.. On the practical solution of the Thue equation. J. Number Theory 31 (1989), 99–132.CrossRefGoogle Scholar
[9]Tzanakis, N. and De Weger, B. M. M.. How to explicitly solve a Thue-Mahler equation. Comp. Math. 84 (1992), 223–288.Google Scholar
[10]De Weger, B. M. M.. Solving exponential diophantine equations using lattice basis reduction algorithms. J. Number Theory 26 (1987), 325–367.CrossRefGoogle Scholar
[11]De Weger, B. M. M.. Algorithms For Diophantine Equations. CWI-Tract, Centre For Mathematics and Computer Science (Amsterdam, 1989).Google Scholar
[12]Zagier, D.. Large integral points on elliptic curves. Math. Comp. 48 (1987), 425–436.CrossRefGoogle Scholar