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arXiv · 1506.03127

Isogenies of non-CM elliptic curves with rational $j$-invariants over number fields

Filip Najman
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Abstract

We unconditionally determine $I_\Q(d)$, the set of possible prime degrees of cyclic $K$-isogneies of elliptic curves with $\Q$-rational $j$-invariants and without complex multiplication over number fields $K$ of degree $\leq d$, for $d\leq 7$, and give an upper bound for $I_\Q(d)$ for $d>7$. Assuming Serre's uniformity conjecture, we determine $I_\Q(d)$ exactly for all positive integers $d$.

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Filip Najman. 2015-06-09. Isogenies of non-CM elliptic curves with rational $j$-invariants over number fields. https://arxiv.org/abs/1506.03127

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