✦ LIBER ✦
On the Existence of Elliptic Curves of Mordell–Weil Rank 6 with Four Parameters
✍ Scribed by Hizuru Yamagishi
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 92 KB
- Volume
- 181
- Category
- Article
- ISSN
- 0021-8693
No coin nor oath required. For personal study only.
✦ Synopsis
We construct an elliptic curve defined over Q with Mordell᎐Weil rank G 6 as a generic twist by a certain quadratic extension. Moreover, since they have four independent parameters, they give us rather a large supply of elliptic curves defined over Q with rank G 6. As an application, we find infinitely many pairs Ž .
a ,b of rational numbers such that the elliptic curve by s x q ax q ax q 1 is of Mordell᎐Weil rank G 6.