On the rank of the elliptic curve \(y^2= x^3+kx\) (Q1281903)
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scientific article; zbMATH DE number 1268562
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the rank of the elliptic curve \(y^2= x^3+kx\) |
scientific article; zbMATH DE number 1268562 |
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On the rank of the elliptic curve \(y^2= x^3+kx\) (English)
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1 September 1999
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\textit{J.-F. Mestre} showed [C. R. Acad. Sci., Paris, Sér. I 314, 919-922 (1992; Zbl 0766.14023)] that there are infinitely many values of \(k\in\mathbb{Q}\), for which the rank of the elliptic curve \(\varepsilon_k:y^2=x^3+kx\) is at least 4. The author improves this result by showing that there are infinitely many \(\varepsilon_k\) of rank at least 5.
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rank
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elliptic curve
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