Publikationsdetails
Towards a Classification of Isolated j-invariants
Abstract
We develop an algorithm to test whether a non-complex multiplication elliptic curve E/Q gives rise to an isolated point of any degree on any modular curve of the form X1(N). This builds on prior work of Zywina which gives a method for computing the image of the adelic Galois representation associated to E. Running this algorithm on all elliptic curves presently in the L-functions and Modular Forms Database and the Stein–Watkins Database gives strong evidence for the conjecture that E gives rise to an isolated point on X1(N) if and only if j(E) = −140625/8,−9317, 351/4, or −162677523113838677.
Details
- Organisationseinheit(en)
-
Institut für Algebra, Zahlentheorie und Diskrete Mathematik
- Externe Organisation(en)
-
Wake Forest University
Brown University
Rijksuniversiteit Groningen (RUG)
Center for Communications Research-La Jolla (CCRL)
Institute for Computational and Experimental Research in Mathematics (ICERM)
Virginia Polytechnic Institute and State University (Virginia Tech)
University of Zagreb
Universität Bayreuth
- Typ
- Artikel
- Journal
- Mathematics of Computation
- Band
- 94
- Seiten
- 447-473
- Anzahl der Seiten
- 27
- ISSN
- 0025-5718
- Publikationsdatum
- 01.2025
- Publikationsstatus
- Veröffentlicht
- Peer-reviewed
- Ja
- ASJC Scopus Sachgebiete
- Algebra und Zahlentheorie, Computational Mathematics, Angewandte Mathematik
- Elektronische Version(en)
-
https://doi.org/10.48550/arXiv.2311.07740 (Zugang:
Offen
)
https://doi.org/10.1090/mcom/3956 (Zugang: Geschlossen )
