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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Construction of elliptic curves with large rank


Author: Thomas J. Kretschmer
Journal: Math. Comp. 46 (1986), 627-635
MSC: Primary 11G05; Secondary 14G25
MathSciNet review: 829634
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Abstract: We describe an algorithm for finding elliptic curves over Q with large rank and nontrivial torsion group. In particular, an example of a curve of rank exactly 10 with a point of order 2 is given. This method seems to suggest that the rank may be large independently of the torsion group.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1986-0829634-8
PII: S 0025-5718(1986)0829634-8
Article copyright: © Copyright 1986 American Mathematical Society