Peer-reviewedCC BY-NC-ND 4.0Mathematics of Computation
Computing with necklaces on elliptic curves
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 ℓ ∕ = p two rational points with complex multiplication can have equal reduction modulo ℓ.
Related
- Computing the Iwasawa μ-Invariants for Elliptic Curves over ℤ2-Extensions
- Torsion points in families of elliptic curves
- $2$-adic Representations of Elliptic Curves over ℚ2
- A motivic Vojta inequality for non-CM elliptic curves with unbounded height
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BibTeX
@article{rebolledo2026computing,
title = {{Computing with necklaces on elliptic curves}},
author = {Marusia Rebolledo and Christian Wuthrich},
journal = {Mathematics of Computation},
year = {2026},
month = sep,
doi = {10.1090/mcom/4279},
eprint = {2509.01816},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05780450v1},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - JOUR
TI - Computing with necklaces on elliptic curves
AU - Marusia Rebolledo
AU - Christian Wuthrich
PY - 2026
DA - 2026/09/19
JO - Mathematics of Computation
DO - 10.1090/mcom/4279
UR - https://hal.science/hal-05780450v1
AB - 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 ℓ ∕ = p two rational points with complex multiplication can have equal reduction modulo ℓ.
SN - 0025-5718
SN - 1088-6842
ER -