engleski

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

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

elliptic curves ; isogenies

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