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High rank elliptic curves with torsion group  |
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| Authors: | Juliá n Aguirre Fernando Castañ eda Juan Carlos Peral |
| Institution: | Departamento de Matemáticas, Universidad del País Vasco, Aptdo. 644, 48080 Bilbao, Spain ; Departamento de Matemáticas, Universidad del País Vasco, Aptdo. 644, 48080 Bilbao, Spain ; Departamento de Matemáticas, Universidad del País Vasco, Aptdo. 644, 48080 Bilbao, Spain |
| Abstract: | We develop an algorithm for bounding the rank of elliptic curves in the family  , all of them with torsion group  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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