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Isogenies of non-CM elliptic curves with rational j-invariants over number fields
Published online by Cambridge University Press: 01 March 2017
Abstract
We unconditionally determine $I_{\mathbb Q}(d)$, the set of possible prime degrees of cyclic K-isogenies of elliptic curves with ${\mathbb Q}$-rational j-invariants and without complex multiplication over number fields K of degree ≤ d, for d ≤ 7, and give an upper bound for $I_{\mathbb Q}(d)$ for d > 7. Assuming Serre's uniformity conjecture, we determine $I_{\mathbb Q}(d)$ exactly for all positive integers d.
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- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 164 , Issue 1 , January 2018 , pp. 179 - 184
- Copyright
- Copyright © Cambridge Philosophical Society 2017
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