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The integer points on three related elliptic curves


Authors: Andrew Bremner and Patrick Morton
Journal: Math. Comp. 39 (1982), 235-238
MSC: Primary 10B10; Secondary 94B60
DOI: https://doi.org/10.1090/S0025-5718-1982-0658228-9
MathSciNet review: 658228
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Abstract: The integer points on the three elliptic curves $ {y^2} = 4c{x^3} + 13$, $ c = 1,3,9$ are found, with an application to coding theory. It is also shown that there are precisely three nonisomorphic cubic extensions of the rationals with discriminant $ - {3^5} \cdot 13$.


References [Enhancements On Off] (What's this?)

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  • [2] H. Hasse, "Arithmetische Theorie der kubischen Zahlkörper auf klassenkörpertheoretischer Grundlage," Math. Z., v. 31, 1930, pp. 565-582. MR 1545136
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  • [5] Th. Skolem, Ein Verfahren zur Behandlung gewisser exponentialer Gleichunger, 8de Skad. mat. Kongr. Forh. Stockholm, 1934.
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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1982-0658228-9
Article copyright: © Copyright 1982 American Mathematical Society

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