Papers › Towards a classification of isolated j-invariants
Towards a classification of isolated j-invariants
Abbey Bourdon, Sachi Hashimoto, Timo Keller, Zev Klagsbrun, David Lowry-Duda, Travis Morrison, Filip Najman, Himanshu Shukla
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
We develop an algorithm to test whether a non-CM 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.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections