On the rank of elliptic curves with three rational points of order 2. II (Q1387923)
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scientific article; zbMATH DE number 1160940
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the rank of elliptic curves with three rational points of order 2. II |
scientific article; zbMATH DE number 1160940 |
Statements
On the rank of elliptic curves with three rational points of order 2. II (English)
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7 February 1999
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The author improves the result of Part I [\textit{S. Kihara} Proc. Japan Acad., Ser. A 73, No. 5, 77-78 (1997; Zbl 0906.11024)]. He proves that there exist infinitely many elliptic curves defined over \(\mathbb{Q}\) with rank \(\geq 5\) with the \(2\)-division subgroup \(\mathbb{Q}\)-rational. The construction is explicit.
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elliptic curves over global fields
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Mordell-Weil group
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\(\mathbb{Q}\)-rational 2-division subgroup
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