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1996 | 77 | 4 | 385-404
Tytuł artykułu

Explicit 4-descents on an elliptic curve

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
Słowa kluczowe
Czasopismo
Rocznik
Tom
77
Numer
4
Strony
385-404
Opis fizyczny
Daty
wydano
1996
otrzymano
1996-03-05
Twórcy
  • Institute of Mathematics and Statistics, University of Kent at Canterbury, Canterbury, Kent, England
autor
  • Institute of Mathematics and Statistics, University of Kent at Canterbury, Canterbury, Kent, England
autor
  • Institute of Mathematics and Statistics, University of Kent at Canterbury, Canterbury, Kent, England
Bibliografia
  • [1] B. J. Birch and H. P. F. Swinnerton-Dyer, Notes on elliptic curves. I, J. Reine Angew. Math. 212 (1963), 7-25.
  • [2] B. J. Birch and H. P. F. Swinnerton-Dyer, Notes on elliptic curves. II, J. Reine Angew. Math. 218 (1965), 79-108.
  • [3] A. Bremner, On the equation y² = x(x²+p), in: Number Theory and Applications, R. A. Mollin (ed.), Kluwer, Dordrecht, 1989, 3-23.
  • [4] A. Bremner and J. W. S. Cassels, On the equation y² = x(x²+p), Math. Comp. 42 (1984), 257-264.
  • [5] J. W. S. Cassels, Diophantine equations with special reference to elliptic curves, J. London Math. Soc. 41 (1966), 193-291.
  • [6] J. W. S. Cassels, The Mordell-Weil group of curves of genus 2, in: Arithmetic and Geometry Papers Dedicated to I. R. Shafarevich on the Occasion of his Sixtieth Birthday, Vol. 1, Birkhäuser, 1983, 29-60.
  • [7] J. W. S. Cassels, Local Fields, London Math. Soc. Student Texts, Cambridge University Press, 1986.
  • [8] J. W. S. Cassels, Lectures on Elliptic Curves, London Math. Soc. Student Texts, Cambridge University Press, 1991.
  • [9] H. Cohen, A Course in Computational Algebraic Number Theory, Springer, Berlin, 1993.
  • [10] I. Connell, Addendum to a paper of Harada and Lang, J. Algebra 145 (1992), 463-467.
  • [11] J. E. Cremona, Algorithms for Modular Elliptic Curves, Cambridge University Press, 1992.
  • [12] J. Gebel, A. Pethő and H. G. Zimmer, Computing integral points on elliptic curves, Acta. Arith. 68 (1994), 171-192.
  • [13] 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 Proc. Lecture Notes 4, Amer. Math. Soc., 1994.
  • [14] M. J. Greenberg, Lectures on Forms in Many Variables, W. A. Benjamin, 1969.
  • [15] W. H. Greub, Linear Algebra, Springer, 1967.
  • [16] M. J. Razar, A relation between the two component of the Tate-Šafarevič group and L(1) for certain elliptic curves, Amer. J. Math. 96 (1974), 127-144.
  • [17] S. Siksek, Descents on Curves of Genus 1, PhD thesis, Exeter University, 1995.
  • [18] S. Siksek, Infinite descent on elliptic curves, Rocky Mountain J. Math. 25 (1995), 1501-1538.
  • [19] S. Siksek and N. P. Smart, On the complexity of computing the 2-Selmer group of an elliptic curve, preprint, 1995.
  • [20] J. H. Silverman, The Arithmetic of Elliptic Curves, Springer, 1986.
  • [21] N. P. Smart, S-integral points on elliptic curves, Proc. Cambridge Philos. Soc. 116 (1994), 391-399.
  • [22] N. P. Smart and N. M. Stephens, Integral points on elliptic curves over number fields, Proc. Cambridge Philos. Soc., to appear, 1996.
  • [23] R. J. Stroeker and N. Tzanakis, Solving elliptic diophantine equations by estimating linear forms in elliptic logarithms, Acta. Arith. 67 (1994), 177-196.
  • [24] H. P. F. Swinnerton-Dyer, Rational zeros of two quadratic forms, Acta. Arith. 9 (1964), 261-270.
  • [25] J. A. Todd, Projective and Analytical Geometry, Pitman, 1947.
  • [26] A. Weil, Number Theory. An Approach Through History, Birkhäuser, 1984.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-aav77i4p385bwm
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