Publication details
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
- Organisation(s)
-
Institute of Algebra, Number Theory and Discrete Mathematics
- External Organisation(s)
-
Wake Forest University
Brown University
University of Groningen (UG)
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
University of Bayreuth
- Type
- Article
- Journal
- Mathematics of Computation
- Volume
- 94
- Pages
- 447-473
- No. of pages
- 27
- ISSN
- 0025-5718
- Publication date
- 01.2025
- Publication status
- Published
- Peer reviewed
- Yes
- ASJC Scopus subject areas
- Algebra and Number Theory, Computational Mathematics, Applied Mathematics
- Electronic version(s)
-
https://doi.org/10.48550/arXiv.2311.07740 (Access:
Open
)
https://doi.org/10.1090/mcom/3956 (Access: Closed )
