Elliptic curves of conductor 11

M. K. Agrawal; J. H. Coates; D. C. Hunt; A. J. Vanderpoorten

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

Elliptic curves of conductor 11

M. K. Agrawal^*, J. H. Coates, D. C. Hunt, A. J. Vanderpoorten

^*Corresponding author for this work

Macquarie University Administration Unit

Research output: Contribution to journal › Article › peer-review

12 Citations (Scopus)

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 ThueMahler 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.

Original language	English
Pages (from-to)	991-1002
Number of pages	12
Journal	Mathematics of Computation
Volume	35
Issue number	151
DOIs	https://doi.org/10.1090/S0025-5718-1980-0572871-5
Publication status	Published - 1980

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title = "Elliptic curves of conductor 11",

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 ThueMahler 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.",

author = "Agrawal, {M. K.} and Coates, {J. H.} and Hunt, {D. C.} and Vanderpoorten, {A. J.}",

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AU - Agrawal, M. K.

AU - Coates, J. H.

AU - Hunt, D. C.

AU - Vanderpoorten, A. J.

PY - 1980

Y1 - 1980

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AB - 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 ThueMahler 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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Elliptic curves of conductor 11

Abstract

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