Infinite Families Of Isogeny-Torsion Graphs
Garen Chiloyan

TL;DR
This paper classifies isogeny-torsion graphs of elliptic curves over rationals, identifying which graphs correspond to infinitely many j-invariants, thus advancing understanding of elliptic curve isogeny structures.
Contribution
It provides a complete classification of isogeny-torsion graphs associated with elliptic curves over b4, determining which graphs occur infinitely often.
Findings
Identifies isogeny-torsion graphs with infinitely many j-invariants.
Classifies all possible isogeny-torsion graph structures over b4.
Establishes criteria linking graph structure to infinite families.
Abstract
Let be a -isogeny class of elliptic curves defined over . The isogeny graph associated to is a graph which has a vertex for each element of and an edge for each -isogeny of prime degree that maps one element of to another element of , with the degree recorded as a label of the edge. The isogeny-torsion graph associated to is the isogeny graph associated to where, in addition, we label each vertex with the abstract group structure of the torsion subgroup over of the corresponding elliptic curve. The main result of the article is a determination of which isogeny-torsion graphs associated to -isogeny classes of elliptic curves defined over correspond to infinitely many -invariants.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsFinite Group Theory Research · Geometric and Algebraic Topology
