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Computing S-integral points on elliptic curves

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Algorithmic Number Theory (ANTS 1996)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1122))

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References

  1. D. Bertrand, Approximations diophantiennes p-adiques sur les courbes elliptiques admettant und multiplication complexe. Comp. Math. 37 (1978), 21–50.

    Google Scholar 

  2. S. David, Minorations de formes linéaires de logarithmes elliptiques. To appear in Mém. Soc. Math. Prance.

    Google Scholar 

  3. J. Gebel, Bestimmung aller ganzen und S-ganzen Punkte auf elliptischen Kurven über den rationalen Zahlen mit Anwendung auf die Mordellschen Kurven. PhD Thesis, Saarbrücken 1996.

    Google Scholar 

  4. J. Gebel, A. Pethö and H.G. Zimmer, Computing integral points on elliptic curves. Acta Arith. 68 (1994), 171–192.

    Google Scholar 

  5. J. Gebel, A. Pethö and H.G. Zimmer, On Mordell's equation. To appear.

    Google Scholar 

  6. J. Gebel, A. Pethö and H.G. Zimmer, Computing integral points on Mordell's elliptic curves. To appear in Proc. Journées Arithmétiques, Barcelona 1995.

    Google Scholar 

  7. G. Rémond and F. Urfels, Approximation diophantienne de logarithmes elliptiques p-adiques. J. Numb. Th. 57 (1996), 133–169.

    Google Scholar 

  8. J.H. Silverman, The Arithmetic of Elliptic Curves. Grad. Texts in Math. 106, Springer-Verlag, Heidelberg 1986.

    Google Scholar 

  9. N.P. Smart, S-integral points on elliptic curves. Math. Proc. Camb. Phil. Soc. 116 (1994), 391–399.

    Google Scholar 

  10. R.J. Stroeker and N. Tzanakis, Solving elliptic diophantine equations by estimating linear forms in elliptic logarithms. Acta Arith. 67 (1994), 177–196.

    Google Scholar 

  11. B.M.M. de Weger, Algorithms for diophantine equations. PhD Thesis. Amsterdam 1987.

    Google Scholar 

  12. H.G. Zimmer, A Limit Formula for the Canonical Height of an Elliptic Curve and its Application to Height Computations. “Number Theory”. Proc. First Conf. CNTA, ed. by R. Mollin. W. de Gruyter, Berlin 1990, 641–659.

    Google Scholar 

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Henri Cohen

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© 1996 Springer-Verlag Berlin Heidelberg

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Gebel, J., Pethő, A., Zimmer, H.G. (1996). Computing S-integral points on elliptic curves. In: Cohen, H. (eds) Algorithmic Number Theory. ANTS 1996. Lecture Notes in Computer Science, vol 1122. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61581-4_52

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  • DOI: https://doi.org/10.1007/3-540-61581-4_52

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  • Print ISBN: 978-3-540-61581-1

  • Online ISBN: 978-3-540-70632-8

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