Local-global principle for isogenies of elliptic curves over quadratic fields

29 Jan 2025  ·  Stevan Gajović, Jeroen Hanselman, Angelos Koutsianas ·

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 $X_{D_{10}}(11)$.

PDF Abstract