Elliptic curves of conductor 11-Reference-Cited by-同舟云学术

Elliptic curves of conductor 11

Published:1980 Issue:151 Volume:35 Page:991-1002
ISSN:0025-5718
Container-title:Mathematics of Computation
language:en
Short-container-title:Math. Comp.

Author:

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

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.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Link

http://www.ams.org/mcom/1980-35-151/S0025-5718-1980-0572871-5/S0025-5718-1980-0572871-5.pdf

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