A Classification of Isogeny-Torsion Graphs of Elliptic Curves Defined over the Rationals

Abstract: An isogeny graph is a nice visualization of the isogeny class of an elliptic curve. A theorem of Kenku shows sharp bounds on the number of distinct isogenies that a rational elliptic curve can have (in particular, every isogeny graph has at most 8 vertices). In this talk, we give a complete classification of the torsion subgroups over $\mathbb{Q}$ that can occur in each vertex of a given isogeny graph of elliptic curves defined over the rationals. This is joint work with \'Alvaro Lozano-Robledo.

number theory

Audience: researchers in the discipline

Comments: Please register for the talks on August 24 here: virginia.zoom.us/meeting/register/tJMkc-uorT8iHdOXRaBkci8wHoKUkqiXaq-E

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POINT: New Developments in Number Theory

Series comments: There will be two 20-minute contributed talks during each meeting aimed at a general number theory audience, including graduate students.

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