Local-global principle for 11-isogenies of elliptic curves is true over quadratic fields

In this paper, we prove that the local-global principle for 11 11 -isogenies for elliptic curves over quadratic fields holds. This gives a positive answer to a conjecture by Banwait and Cremona \cite[Conjecture 1.14]BanwaitCremona14. The proof is based on the determination of the set of quadratic points on the modular curve X D 10 ( 11 ) X_{D_{10}}(11) .

Metadaten
Author:	Stevan Gajović, Jeroen Hanselman, Angelos Koutsianas
URL:	https://pubs.ams.org/ebooks/conm/840
DOI:	https://doi.org/10.1090/conm/840/16813
ISBN:	978-1-4704-8570-2
ISBN:	978-1-4704-8032-5
Parent Title (English):	LuCaNT: Databases, Algorithms, and Computational Number Theory
Secondary publication (full text):	https://doi.org/10.48550/arXiv.2501.17602
Publisher:	American Mathematical Society
Place of publication:	Providence, Rhode Island
Editor:	John W. Jones, Jennifer Paulhus, Andrew W. Sutherland, John Voight
Document Type:	Conference Proceeding
Language:	English
Publication year:	2026
Year of first Publication:	2026
Release Date:	2026/09/24
Page Number:	12
First Page:	155
Last Page:	166
Faculties / Organisational entities:	RPTU in Kaiserslautern / Fachbereich Mathematik / Schwerpunkt Algebra, Geometrie und Computeralgebra / AG Algebra, Geometrie und Computeralgebra
Open access state:	Grün Open-Access
RPTU:	Kaiserslautern
Created at the RPTU:	Yes