On the rank of the elliptic curve \(y^ 2=x^ 3+k\) (Q1093697)
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 \(y^ 2=x^ 3+k\) |
scientific article; zbMATH DE number 4023467
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the rank of the elliptic curve \(y^ 2=x^ 3+k\) |
scientific article; zbMATH DE number 4023467 |
Statements
On the rank of the elliptic curve \(y^ 2=x^ 3+k\) (English)
0 references
1987
0 references
Consider the elliptic curve (*) \(y^ 2=x^ 3+k\) with \(k\in {\mathbb{Q}}(p,q)\). k is an explicitly constructed polynomial of degree \(24\) in p and q with rational coefficients, too complicated to state here. The author claims that for this specific k the curve (*) over \({\mathbb{Q}}(p,q)\) has rank at least 5 [see also the author's paper in Proc. Japan Acad., Ser. 63, 13-16 (1987; Zbl 0614.10017)].
0 references
elliptic curve
0 references
rank
0 references
