Mathematics of Computation

Author(s): Julián Aguirre; Fernando Castañeda; Juan Carlos Peral.
Journal: Math. Comp. 73 (2004), 323-331.
MSC (2000): Primary 11Y50
Posted: May 30, 2003
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Abstract: We develop an algorithm for bounding the rank of elliptic curves in the family $y^2=x^3-B\,x$ , all of them with torsion group $\mathbb{Z} /(2\,\mathbb{Z} )$ and modular invariant

. We use it to look for curves of high rank in this family and present four such curves of rank

and

of rank

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Julián Aguirre
Affiliation: Departamento de Matemáticas, Universidad del País Vasco, Aptdo. 644, 48080 Bilbao, Spain
Email: mtpagesj@lg.ehu.es

Fernando Castañeda
Affiliation: Departamento de Matemáticas, Universidad del País Vasco, Aptdo. 644, 48080 Bilbao, Spain
Email: mtpcabrf@lg.ehu.es

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