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ArticleOriginal scientific text

Title

Canonical heights on the Jacobians of curves of genus 2 and the infinite descent

Authors 1, 2

Affiliations

  1. Department of Pure Mathematics, Liverpool University, P.O. Box 147, Liverpool, L69 3BX, U.K.
  2. Institute of Mathematics and Statistics, University of Kent at Canterbury, Canterbury, Kent, CT2 7NF, U.K.

Bibliography

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  2. J. W. S. Cassels and E. V. Flynn, Prolegomena to a Middlebrow Arithmetic of Curves of Genus 2, Cambridge University Press, 1996.
  3. J. E. Cremona, Algorithms for Modular Elliptic Curves, Cambridge University Press, 1992.
  4. E. V. Flynn, The Jacobian and formal group of a curve of genus 2 over an arbitrary ground field, Proc. Cambridge Philos. Soc. 107 (1990), 425-441.
  5. E. V. Flynn, The group law on the Jacobian of a curve of genus 2, J. Reine Angew. Math. 439 (1993), 45-69.
  6. E. V. Flynn, Descent via isogeny in dimension 2, Acta Arith. 66 (1994), 23-43.
  7. E. V. Flynn, An explicit theory of heights, Trans. Amer. Math. Soc. 347 (1995), 3003-3015.
  8. E. V. Flynn, B. Poonen, and E. F. Schaefer, Cycles of quadratic polynomials and rational points on a genus 2 curve, preprint, 1996.
  9. B. Gross, Local heights on curves, in: Arithmetic Geometry, G. Cornell and J. H. Silverman (eds.), Springer, 1986, 327-339.
  10. S. Lang, Fundamentals of Diophantine Geometry, Springer, 1983.
  11. M. Pohst and H. Zassenhaus, Algorithmic Algebraic Number Theory, Cambridge University Press, 1989.
  12. E. F. Schaefer, 2-descent on the Jacobians of hyperelliptic curves, J. Number Theory 51 (1995), 219-232.
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  14. S. Siksek, Infinite descent on elliptic curves, Rocky Mountain J. Math. 25 (1995), 1501-1538.
  15. J. H. Silverman, The Arithmetic of Elliptic Curves, Springer, 1986.
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  17. J. H. Silverman, The difference between the Weil height and the canonical height on elliptic curves, Math. Comp. 55 (1990), 723-743.
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Acta Arithmetica
1997/79/4
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Pages:
333-352
Main language of publication
English
Received
1996-06-28
Accepted
1996-12-02
Published
1997
Exact and natural sciences