High rank elliptic curves with torsion group $\mathbb {Z}/(2\mathbb {Z})$
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- by Julián Aguirre, Fernando Castañeda and Juan Carlos Peral;
- Math. Comp. 73 (2004), 323-331
- DOI: https://doi.org/10.1090/S0025-5718-03-01547-3
- Published electronically: 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 $j=1728$. We use it to look for curves of high rank in this family and present four such curves of rank $13$ and $22$ of rank $12$.References
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Bibliographic Information
- 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
- Juan Carlos Peral
- Affiliation: Departamento de Matemáticas, Universidad del País Vasco, Aptdo. 644, 48080 Bilbao, Spain
- MR Author ID: 137825
- Email: mtppealj@lg.ehu.es
- Received by editor(s): November 28, 2000
- Received by editor(s) in revised form: July 5, 2002
- Published electronically: May 30, 2003
- Additional Notes: The second and third authors were supported by a grant from the University of the Basque Country.
- © Copyright 2003 American Mathematical Society
- Journal: Math. Comp. 73 (2004), 323-331
- MSC (2000): Primary 11Y50
- DOI: https://doi.org/10.1090/S0025-5718-03-01547-3
- MathSciNet review: 2034125