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Isogenies of non-CM elliptic curves with rational j-invariants over number fields.
- Source :
-
Mathematical Proceedings of the Cambridge Philosophical Society . Jan2018, Vol. 164 Issue 1, p179-184. 6p. - Publication Year :
- 2018
-
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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 03050041
- Volume :
- 164
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Mathematical Proceedings of the Cambridge Philosophical Society
- Publication Type :
- Academic Journal
- Accession number :
- 126608639
- Full Text :
- https://doi.org/10.1017/S0305004117000160