Papers › Lower bounds for the modified Szpiro ratio
Lower bounds for the modified Szpiro ratio
Alexander J. Barrios
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.
Let E/ℚ be an elliptic curve. The modified Szpiro ratio of E is the quantity σₘ(E) =logmax{ |c₄³|,c₆²} /logN_E where c₄ and c₆ are the invariants associated to a global minimal model of E, and N_E denotes the conductor of E. In this article, we show that for each of the fifteen torsion subgroups T allowed by Mazur's Torsion Theorem, there is a rational number l_T such that if T↪E(ℚ) ₜₒᵣₛ, then σₘ(E) >l_T. We also show that this bound is sharp.
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