An extremal prime $p$ for an elliptic curve $E$ is one for which the trace of the Frobenius at $p$ is maximal or minimal in view of the Hasse bound. In this talk, assuming GRH, we present a joint distribution result involving the Chebotarev Density Theorem. As a consequence, we obtain an upper bound for the number of primes satisfying the maximality condition mod $L$ for a sufficiently large prime $L$. This is joint work with Amita Malik.
Extremal Primes for elliptic curves*
Neha Prabhu, Savitribai Phule Pune University, India
2022 AWM Research Symposium
New Directions in Number Theory