A parametric family of elliptic curves

Andrej Dujella

Acta Arithmetica (2000)

  • Volume: 94, Issue: 1, page 87-101
  • ISSN: 0065-1036

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Dujella, Andrej. "A parametric family of elliptic curves." Acta Arithmetica 94.1 (2000): 87-101. <http://eudml.org/doc/207426>.

@article{Dujella2000,
author = {Dujella, Andrej},
journal = {Acta Arithmetica},
keywords = {elliptic curves; integer points; Mordell-Weil rank; integral points},
language = {eng},
number = {1},
pages = {87-101},
title = {A parametric family of elliptic curves},
url = {http://eudml.org/doc/207426},
volume = {94},
year = {2000},
}

TY - JOUR
AU - Dujella, Andrej
TI - A parametric family of elliptic curves
JO - Acta Arithmetica
PY - 2000
VL - 94
IS - 1
SP - 87
EP - 101
LA - eng
KW - elliptic curves; integer points; Mordell-Weil rank; integral points
UR - http://eudml.org/doc/207426
ER -

References

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  2. [2] A. Bremner, R. J. Stroeker and N. Tzanakis, On sums of consecutive squares, J. Number Theory 62 (1997), 39-70. Zbl0876.11024
  3. [3] J. E. Cremona, Algorithms for Modular Elliptic Curves, Cambridge Univ. Press, 1997. Zbl0872.14041
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  5. [5] A. Dujella, The problem of the extension of a parametric family of Diophantine triples, Publ. Math. Debrecen 51 (1997), 311-322. Zbl0903.11010
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  7. [7] A. Dujella, Diophantine triples and construction of high-rank elliptic curves over ℚ with three non-trivial 2-torsion points, Rocky Mountain J. Math., to appear. Zbl0989.11032
  8. [8] A. Dujella and A. Pethő, Generalization of a theorem of Baker and Davenport, Quart. J. Math. Oxford Ser. (2) (49) (1998), 291-306. Zbl0911.11018
  9. [9] A. Dujella and A. Pethő, Integer points on a family of elliptic curves, Publ. Math. Debrecen, to appear. 
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  13. [13] C. M. Grinstead, On a method of solving a class of Diophantine equations, Math. Comp. 32 (1978), 936-940. Zbl0389.10015
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  15. [15] A. Knapp, Elliptic Curves, Princeton Univ. Press, 1992. 
  16. [16] T. Nagell, Introduction to Number Theory, Almqvist, Stockholm; Wiley, New York, 1951. Zbl0042.26702
  17. [17] T. Nagell, Contributions to the theory of a category of Diophantine equations of the second degree with two unknowns, Nova Acta Soc. Sci. Upsal. 16 (1954), 1-38. Zbl0057.28304
  18. [18] I. Niven, H. S. Zuckerman and H. L. Montgomery, An Introduction to the Theory of Numbers, Wiley, New York, 1991. Zbl0742.11001
  19. [19] K. Ono, Euler's concordant forms, Acta Arith. 78 (1996), 101-123. 
  20. [20] J. H. Rickert, Simultaneous rational approximations and related diophantine equations, Math. Proc. Cambridge Philos. Soc. 113 (1993), 461-472. Zbl0786.11040
  21. [21] J. H. Silverman, Rational points on elliptic surfaces, preprint. Zbl0752.14034
  22. [22] SIMATH manual, Universität des Saarlandes, Saarbrücken, 1997. 

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