---
_id: '60874'
abstract:
- lang: eng
  text: Given a number field, it is an important question in algorithmic number theory
    to determine all its subfields. If the search is restricted to abelian subfields,
    one can try to determine them by using class field theory. For this, it is necessary
    to know the ramified primes. We show that the ramified primes of the subfield
    can be computed efficiently. Using this information we give algorithms to determine
    all the quadratic and the cyclic cubic subfields of the initial field. The approach
    generalises to cyclic subfields of prime degree. In the case of quadratic subfields,
    our approach is much faster than other methods.
article_number: '100039'
author:
- first_name: Andreas-Stephan
  full_name: Elsenhans, Andreas-Stephan
  last_name: Elsenhans
- first_name: Jürgen
  full_name: Klüners, Jürgen
  id: '21202'
  last_name: Klüners
citation:
  ama: Elsenhans A-S, Klüners J. Computing quadratic subfields of number fields. <i>Journal
    of Computational Algebra</i>. 2025;15. doi:<a href="https://doi.org/10.1016/j.jaca.2025.100039">10.1016/j.jaca.2025.100039</a>
  apa: Elsenhans, A.-S., &#38; Klüners, J. (2025). Computing quadratic subfields of
    number fields. <i>Journal of Computational Algebra</i>, <i>15</i>, Article 100039.
    <a href="https://doi.org/10.1016/j.jaca.2025.100039">https://doi.org/10.1016/j.jaca.2025.100039</a>
  bibtex: '@article{Elsenhans_Klüners_2025, title={Computing quadratic subfields of
    number fields}, volume={15}, DOI={<a href="https://doi.org/10.1016/j.jaca.2025.100039">10.1016/j.jaca.2025.100039</a>},
    number={100039}, journal={Journal of Computational Algebra}, publisher={Elsevier
    BV}, author={Elsenhans, Andreas-Stephan and Klüners, Jürgen}, year={2025} }'
  chicago: Elsenhans, Andreas-Stephan, and Jürgen Klüners. “Computing Quadratic Subfields
    of Number Fields.” <i>Journal of Computational Algebra</i> 15 (2025). <a href="https://doi.org/10.1016/j.jaca.2025.100039">https://doi.org/10.1016/j.jaca.2025.100039</a>.
  ieee: 'A.-S. Elsenhans and J. Klüners, “Computing quadratic subfields of number
    fields,” <i>Journal of Computational Algebra</i>, vol. 15, Art. no. 100039, 2025,
    doi: <a href="https://doi.org/10.1016/j.jaca.2025.100039">10.1016/j.jaca.2025.100039</a>.'
  mla: Elsenhans, Andreas-Stephan, and Jürgen Klüners. “Computing Quadratic Subfields
    of Number Fields.” <i>Journal of Computational Algebra</i>, vol. 15, 100039, Elsevier
    BV, 2025, doi:<a href="https://doi.org/10.1016/j.jaca.2025.100039">10.1016/j.jaca.2025.100039</a>.
  short: A.-S. Elsenhans, J. Klüners, Journal of Computational Algebra 15 (2025).
date_created: 2025-08-05T07:01:39Z
date_updated: 2025-08-05T07:10:25Z
doi: 10.1016/j.jaca.2025.100039
external_id:
  arxiv:
  - '1907.13383'
intvolume: '        15'
language:
- iso: eng
publication: Journal of Computational Algebra
publication_identifier:
  issn:
  - 2772-8277
publication_status: published
publisher: Elsevier BV
status: public
title: Computing quadratic subfields of number fields
type: journal_article
user_id: '82981'
volume: 15
year: '2025'
...