Papers › Explicit classification of isogeny graphs of rational elliptic curves
Explicit classification of isogeny graphs of rational elliptic curves
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 n>1 be an integer such that X₀( n) has genus $0$, and let K be a field of characteristic $0$ or relatively prime to 6n. In this article, we explicitly classify the isogeny graphs of all rational elliptic curves that admit a non-trivial isogeny over ℚ. We achieve this by introducing $56$ parameterized families of elliptic curves 𝒞_(n,i)(t,d) defined over K(t,d), which have the following two properties for a fixed n: the elliptic curves 𝒞_(n,i)(t,d) are isogenous over K(t,d), and there are integers k₁ and k₂ such that the j-invariants of 𝒞_(n,k₁)(t,d) and 𝒞_(n,k₂)(t,d) are given by the Fricke parameterizations. As a consequence, we show that if E is an elliptic curve over a number field K with isogeny class degree divisible by n∈{4,6,9}, then there is a quadratic twist of E that is semistable at all primes 𝔭 of K such that 𝔭∤n.
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