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Mathematics of Computation

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Ideal 9th-order multigrades and Letac's elliptic curve


Author: C. J. Smyth
Journal: Math. Comp. 57 (1991), 817-823
MSC: Primary 11D72; Secondary 11G05
DOI: https://doi.org/10.1090/S0025-5718-1991-1094960-9
MathSciNet review: 1094960
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Abstract: By showing that the elliptic curve $ ({x^2} - 13)({y^2} - 13) = 48$ has infinitely many rational points, we prove that Letac's construction produces infinitely many genuinely different ideal 9th-order multigrades. We give one (not very small) new example, and, by finding the Mordell-Weil group of the curve, show how to find all examples obtainable by Letac's method.


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DOI: https://doi.org/10.1090/S0025-5718-1991-1094960-9
Article copyright: © Copyright 1991 American Mathematical Society

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