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

Smyth, C. J.

doi:10.1090/S0025-5718-1991-1094960-9

Ideal 9th-order multigrades and Letac’s elliptic curve
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Math. Comp. 57 (1991), 817-823 Request permission

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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Solution de quelque problèmes dans la théorie arithmétique des cubiques planes du premier genre

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