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A family of elliptic curves and cyclic cubic field extensions*

  • E. Thomas (a1) and A.T. Vasquez (a2)

Let K be a field with char K ≡ 2,3. We consider the problem of finding rational points over K on the family of elliptic curves Fλ, given in homogeneous coordinates (over ) by

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[1] Caldwell, C.. Thesis, University of California (Berkeley), 1984.
[2] Craig, M.. Integer values of H(x*/yz). J. Number Theory 10 (1978), 6263.
[3] Dofs, E.. On some classes of homogeneous ternary cubic diophantine equations. Ark. Mat. 13 (1975), 2972.
[4] Hubwitz, A.. Über ternare diophantische Gleichungen dritten Grades. Math. Werke, 2 (Birk-hauser, 1933), 446468.
[5] Milnor, J. and Stasheff, J.. Characteristic classes. Annals of Math. Studies, vol. 76 (Princeton University Press, 1974).
[6] Mordell, L.. Diophantine Equations. (Academic Press, 1969).
[7] Mordell, L.. On the rational solutions of the indeterminate equations of the 3rd and 4th degree. Proc. Cambridge Philos. Soc. 21 (1922), 179192.
[8] Mordell, L.. The diophantine equation x3 + y3 + z3 + kxyz = 0. Colloque sur la thiorie des nombres (Bruxelles, 1955), 6776.
[9] Thomas, E. and Vasqtjez, A.. Diophantine equations arising from cubic number fields. J. Number Theory 13 (1981), 398414.
[10] Weil, A.. L'arithmetique sur les courbes algébriqes. Acta Math. 52 (1929), 281315.
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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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