On the rank of the elliptic curve \(y^2=x^3+kx\). II (Q1884113)
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scientific article; zbMATH DE number 2109877
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the rank of the elliptic curve \(y^2=x^3+kx\). II |
scientific article; zbMATH DE number 2109877 |
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On the rank of the elliptic curve \(y^2=x^3+kx\). II (English)
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25 October 2004
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The author proves the following two theorems: 1) There is an elliptic curve \(y^2 = x^3 + kx\) defined over \(\mathbb Q(x_1,x_2,x_3)\) with rank \(\geq 6\). 2) There are infinitely many elliptic curves \(y^2 = x^3 + kx\) defined over \(\mathbb Q\) with rank \(\geq 6\). Part I, cf. ibid. 74, No. 7, 115--116 (1998; Zbl 0919.11039).
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elliptic curve
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rank
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