On the rank of elliptic curves with a torsion group isomorphic to \(\mathbb{Z}/5\mathbb{Z}\) (Q2708162)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the rank of elliptic curves with a torsion group isomorphic to \(\mathbb{Z}/5\mathbb{Z}\) |
scientific article |
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12 June 2001
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elliptic curve
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torsion subgroup
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rank
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On the rank of elliptic curves with a torsion group isomorphic to \(\mathbb{Z}/5\mathbb{Z}\) (English)
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By an ingenious construction, the author shows the existence of an elliptic curve defined over \(\mathbb{Q}\) of nonconstant \(j\)-invariant with a torsion subgroup isomorphic to \(\mathbb{Z}/5\mathbb{Z}\) and of rank \(\geq 3\) over \(\mathbb{Q}\). Also the existence is shown by explicit construction of an elliptic curve over \(\mathbb{Q}\) of rank \(\geq 4\) and with torsion subgroup isomorphic to \(\mathbb{Z}/5\mathbb{Z}\).
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