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

2022/03/20 by Borna Vukorepa, Vukorepa, Borna · 3 citations
Mathematics · #Algebraic Geometry and Number Theory

paper · pdf · doi:10.48550/arxiv.2203.10672

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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• The possible adelic indices for elliptic curves admitting a rational cyclic isogeny
• Rational isolated j-invariants from X₁(ℓⁿ) and X₀(ℓⁿ)
• Torsion of \mathbb Q-curves over number fields of small odd prime degree

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