Papers › Local data of rational elliptic curves with non-trivial torsion
Local data of rational elliptic curves with non-trivial torsion
Alexander J. Barrios, Manami Roy
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.
By Mazur's Torsion Theorem, there are fourteen possibilities for the non-trivial torsion subgroup T of a rational elliptic curve. For each T, such that E may have additive reduction at a prime p, we consider a parameterized family E_T of elliptic curves with the property that they parameterize all elliptic curves E/ℚ which contain T in their torsion subgroup. Using these parameterized families, we explicitly classify the Kodaira-N\'{e}ron type, the conductor exponent, and the local Tamagawa number at each prime p where E/ℚ has additive reduction. As a consequence, we find all rational elliptic curves with a $2$-torsion or a $3$-torsion point that have global Tamagawa number $1$.
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