## Number Theory Seminar

### Wednesday, June 20th, 2018

**Time:** 2:00-3:20p.m. **Place:** Jeffery Hall 422

**Speaker:** Neha Prabhu (Queen's University)

**Title:** EXTREMAL PRIMES FOR NON-CM ELLIPTIC CURVES.

**Abstract:** For an elliptic curve E over the field of rationals, the distribution of the number of points on E modulo a prime p has been well-studied over the last few decades. A relatively recent study is that of extremal primes for a given curve E. These are the primes p of good reduction for which the number of points on E mod p is either maximal or minimal. If E is a curve with CM, an asymptotic for the number of extremal primes was determined by James and Pollack. The talk will discuss the non-CM case and focus on obtaining upper bounds. This is joint work with C. David, A. Gafni, A. Malik and C. Turnage-Butterbaugh