On the rank of the elliptic curve \(y^ 2=x^ 3+k\). II (Q1357047)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: On the rank of the elliptic curve \(y^ 2=x^ 3+k\). II |
scientific article; zbMATH DE number 1022275
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the rank of the elliptic curve \(y^ 2=x^ 3+k\). II |
scientific article; zbMATH DE number 1022275 |
Statements
On the rank of the elliptic curve \(y^ 2=x^ 3+k\). II (English)
0 references
2 December 1997
0 references
By construction of the required number of independent points on the Mordell curve \[ y^2= x^3+k, \quad k\in\mathbb{Q}^* \] for certain \(k=k(t)\) depending on a parameter \(t\), the author shows that there are infinitely many non-isomorphic (over \(\mathbb{Q})\) Mordell curves of rank at least 7. This extends previous work of the author [\textit{S. Kihara}, Proc. Japan Acad., Ser. A 63, 76-78 (1987; Zbl 0629.14024)].
0 references
elliptic curve
0 references
Mordell curve
0 references
rank
0 references
