Explicit Arithmetic in Isogeny-Torsion Graphs

Abstract: Let E and E’ be isogenous elliptic curves defined over Q. Then their associated L-functions are equal; in particular, their leading Taylor coefficients are equal. However (assuming the conjecture of Birch and Swinnerton-Dyer), the individual arithmetic invariants that comprise the leading terms may not be. In this talk we explore how the individual BSD terms change under a prime-degree isogeny and how to quantify the “likelihood” that such changes occur. This is joint work with Alexander Barrios.

number theory

Audience: researchers in the topic

Five College Number Theory Seminar