Isogenies over quadratic fields of elliptic curves with rational $j$-invariant

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arxiv 2203.10672 v1 pith:4AMNDJVO submitted 2022-03-20 math.NT

Borna Vukorepa This is my paper · ORCID

classification math.NT

keywords curvesellipticfieldsinvariantisogeniesquadraticrationalcyclic

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abstract

We determine the possible degrees of cyclic isogenies defined over quadratic fields for non-CM elliptic curves with rational $j$-invariant.

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Rational isolated $j$-invariants from $X_1(\ell^n)$ and $X_0(\ell^n)$
math.NT 2025-06 accept novelty 7.0 of 10

For prime-power level, rational isolated j-invariants are exactly 15 values on X_1 (13 CM plus two non-CM) and 19 values on X_0 (13 CM plus six non-CM).