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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 

 

Elliptic curves of conductor $ 11$


Authors: M. K. Agrawal, J. H. Coates, D. C. Hunt and A. J. van der Poorten
Journal: Math. Comp. 35 (1980), 991-1002
MSC: Primary 10D12; Secondary 10B10, 14K07
DOI: https://doi.org/10.1090/S0025-5718-1980-0572871-5
MathSciNet review: 572871
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Abstract: We determine all elliptic curves defined over Q of conductor 11. Firstly, we reduce the problem to one of solving a diophantine equation, namely a certain Thue-Mahler equation. Then we apply recent sharp inequalities for linear forms in the logarithms of algebraic numbers to bound solutions of that equation. Finally, some straightforward computations yield all solutions of the diophantine equation. Our results are in accordance with the conjecture of Taniyama-Weil for conductor 11.


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DOI: https://doi.org/10.1090/S0025-5718-1980-0572871-5
Article copyright: © Copyright 1980 American Mathematical Society