Álvaro Lozano-Robledo – University of Connecticut

Name: Álvaro Lozano-Robledo – University of Connecticut
Start: 2021-02-08T06:15:00-05:00
End: 2021-02-08T07:15:00-05:00
Location: ZOOM

February 8, 2021 @ 6:15 am - 7:15 am EST

Title: A classification of isogeny-torsion graphs for isogeny classes of elliptic curves defined over $\mathbb{Q}$ .

Abstract: A well-known theorem of Mazur says that there are precisely 15 torsion subgroups that occur for elliptic curves defined over $\mathbb{Q}$ . In this talk, we will discuss a generalization of Mazur’s theorem to isogeny classes of elliptic curves over $\mathbb{Q}$ . More concretely, let $E_1,\ldots, E_n$ be the elliptic curves in an isogeny class over $\mathbb{Q}$ . In this talk, we will classify the torsion subgroups that can occur simultaneously for $E_1,\ldots, E_n$ . Further, we define isogeny-torsion graphs to be isogeny graphs where the vertices are marked with the abelian structure of the torsion subgroup of the curve, and we give a full classification of those isogeny-torsion graphs that occur over the rationals. (This is joint work with Garen Chiloyan.)

Details

Date:: February 8, 2021
Time:: 6:15 am - 7:15 am EST
Event Categories:: RTG - Coding, Cryptography and Number Theory (CCNT) Seminar, RTG - Grad Students event

Venue

: ZOOM