Papers › Local-global principle for 11-isogenies of elliptic curves is true over quadratic fields
Local-global principle for 11-isogenies of elliptic curves is true over quadratic fields
Stevan Gajović, Jeroen Hanselman, Angelos Koutsianas
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In this paper, we prove that the local-global principle of $11$-isogenies for elliptic curves over quadratic fields does not fail. This gives a positive answer to a conjecture by Banwait and Cremona. The proof is based on the determination of the set of quadratic points on the modular curve X_(D₁₀)(11).
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