Computing with necklaces on elliptic curves
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913168935092224 |
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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 |