Elliptic curves of conductor 11

Agrawal, M. K.; Coates, J. H.; Hunt, D. C.; van der Poorten, A. J.

doi:10.1090/S0025-5718-1980-0572871-5

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.

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