Explicit 4-descents on an elliptic curve
J. R. Merriman; S. Siksek; N. P. Smart
Acta Arithmetica (1996)
- Volume: 77, Issue: 4, page 385-404
- ISSN: 0065-1036
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topJ. R. Merriman, S. Siksek, and N. P. Smart. "Explicit 4-descents on an elliptic curve." Acta Arithmetica 77.4 (1996): 385-404. <http://eudml.org/doc/206927>.
@article{J1996,
author = {J. R. Merriman, S. Siksek, N. P. Smart},
journal = {Acta Arithmetica},
keywords = {elliptic curves; Computational Number Theory; generators of an elliptic curve; homogeneous space; descent; Tate-Shafarevich group},
language = {eng},
number = {4},
pages = {385-404},
title = {Explicit 4-descents on an elliptic curve},
url = {http://eudml.org/doc/206927},
volume = {77},
year = {1996},
}
TY - JOUR
AU - J. R. Merriman
AU - S. Siksek
AU - N. P. Smart
TI - Explicit 4-descents on an elliptic curve
JO - Acta Arithmetica
PY - 1996
VL - 77
IS - 4
SP - 385
EP - 404
LA - eng
KW - elliptic curves; Computational Number Theory; generators of an elliptic curve; homogeneous space; descent; Tate-Shafarevich group
UR - http://eudml.org/doc/206927
ER -
References
top- [1] B. J. Birch and H. P. F. Swinnerton-Dyer, Notes on elliptic curves. I, J. Reine Angew. Math. 212 (1963), 7-25. Zbl0118.27601
- [2] B. J. Birch and H. P. F. Swinnerton-Dyer, Notes on elliptic curves. II, J. Reine Angew. Math. 218 (1965), 79-108. Zbl0147.02506
- [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. Zbl0531.10014
- [5] J. W. S. Cassels, Diophantine equations with special reference to elliptic curves, J. London Math. Soc. 41 (1966), 193-291. Zbl0138.27002
- [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. Zbl0786.11071
- [10] I. Connell, Addendum to a paper of Harada and Lang, J. Algebra 145 (1992), 463-467. Zbl0759.11021
- [11] J. E. Cremona, Algorithms for Modular Elliptic Curves, Cambridge University Press, 1992. Zbl0758.14042
- [12] J. Gebel, A. Pethő and H. G. Zimmer, Computing integral points on elliptic curves, Acta. Arith. 68 (1994), 171-192. Zbl0816.11019
- [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. Zbl0809.14024
- [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. Zbl0296.14016
- [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. Zbl0852.11028
- [19] S. Siksek and N. P. Smart, On the complexity of computing the 2-Selmer group of an elliptic curve, preprint, 1995. Zbl0915.11032
- [20] J. H. Silverman, The Arithmetic of Elliptic Curves, Springer, 1986. Zbl0585.14026
- [21] N. P. Smart, S-integral points on elliptic curves, Proc. Cambridge Philos. Soc. 116 (1994), 391-399. Zbl0817.11031
- [22] N. P. Smart and N. M. Stephens, Integral points on elliptic curves over number fields, Proc. Cambridge Philos. Soc., to appear, 1996. Zbl0881.11054
- [23] R. J. Stroeker and N. Tzanakis, Solving elliptic diophantine equations by estimating linear forms in elliptic logarithms, Acta. Arith. 67 (1994), 177-196. Zbl0805.11026
- [24] H. P. F. Swinnerton-Dyer, Rational zeros of two quadratic forms, Acta. Arith. 9 (1964), 261-270. Zbl0128.04702
- [25] J. A. Todd, Projective and Analytical Geometry, Pitman, 1947.
- [26] A. Weil, Number Theory. An Approach Through History, Birkhäuser, 1984.
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