Elliptic curves of conductor $11$
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- by M. K. Agrawal, J. H. Coates, D. C. Hunt and A. J. van der Poorten PDF
- Math. Comp. 35 (1980), 991-1002 Request permission
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.References
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Additional Information
- © Copyright 1980 American Mathematical Society
- 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