Supersingular distribution on average for congruence classes of primes

摘要

Given an elliptic curve E defined over a number field F and a prime p of good reduction, let ap = Np + 1 — IE(Fp)I. One says hat p is supersingular for E if ap 0 (mod p). Given Hasse's bound of 2-VNT on lap', this occurs for degree one primes p with Np > 3 if ap = 0.