Full paper in PDF:
$%J. Aguirre, F. Castañeda, and J. C. Peral, High rank elliptic curves of the form y2+x3+Bx, Rev. Mat. Complut. 13 (2000), no. 1, 17–31.%$

High Rank Elliptic Curves of the Form y2+x3+Bx
Julián AGUIRRE, Fernando CASTAÑEDA,
and Juan C. PERAL
Departamento de Matemáticas
Universidad del País Vasco
Aptdo. 644
48080 Bilbao — Spain
mtpagesj@lg.ehu.es  mtpcabrf@lg.ehu.es
mtppealj@lg.ehu.es

Received: March 22, 1999
Revised: July 19, 1999

ABSTRACT

Seven elliptic curves of the form 2 3 y + x + Bx and having rank at least 8 are presented. To find them we use the double descent method of Tate. In particular we prove that the curve with B = -14752493461692 has rank exactly 8.

1991 Mathematics Subject Classification: 11040.