Computing with necklaces on elliptic curves

Fuente: arXiv
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Main Authors: Rebolledo, Marusia, Wuthrich, Christian
Format: Preprint
Published: 2025
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author Rebolledo, Marusia
Wuthrich, Christian
author_facet Rebolledo, Marusia
Wuthrich, Christian
contents 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 $\ell$.
format Preprint
id arxiv_https___arxiv_org_abs_2509_01816
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Computing with necklaces on elliptic curves
Rebolledo, Marusia
Wuthrich, Christian
Number Theory
11G05, 11G18, 11Y99
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 $\ell$.
title Computing with necklaces on elliptic curves
topic Number Theory
11G05, 11G18, 11Y99
url https://arxiv.org/abs/2509.01816