Work

Computing with necklaces on elliptic curves

Year: 2026

Type: article

Abstract: We present computational algorithms to work with points on the modular curve associated to the normaliser of a non-split Cartan group of prime level $p$. Rather than working with explicit equations, we represent these points using the moduli interpretation of necklaces in the $p$-torsion of elliptic curves. We use our methods to investigate for which primes $\ell\neq p$ two rational points with complex multiplication can have equal reduction modulo $\ell$.

Source: Mathematics of Computation

DOI: 10.1090/mcom/4279

Authors: Marusia Rebolledo, Christian Wuthrich

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Funders: Agence Nationale de la Recherche, Engineering and Physical Sciences Research Council

Awards: Approaching the Birch and Swinnerton-Dyer conjecture by counting adelic points, Effective arithmetic geometry in Clermont, Arithmetic of the j-invariant, G9000375798, G9000380841, G9000385268

OpenAlex ID: W4416697813

FWCI: 4.029

Cites: 2

Cited by: 2

Related to: 10