Let E d ( x ) denote the “Euler polynomial” x 2 + x + ( 1 − d ) / 4 if d ≡ 1 ( mod 4 ) and x 2 − d if d ≡ 2 , 3 ( mod 4 ) . Set Ω ( n ) to be the number of prime factors (counting multiplicity) of the positive integer n. The Ono invariant Ono d of K = Q ( d ) is defined to be max { Ω ( E d ( b ) ) : b = 0 , 1 , … , | Δ d | / 4 − 1 } except when d = − 1 , − 3 in which case Ono d is defined to be 1. Finally, let h d = h k denote the class number of K. In 2002 J. Cohen and J. Sonn conjectured that h d = 3 ⇔ Ono d = 3 and − d = p ≡ 3 ( mod 4 ) is a prime. They verified that the conjecture is true for p < 1.5 × 10 7 . Moreover, they proved that the conjecture holds for p > 10 17 assuming the extended Riemann Hypothesis. In this paper, we show that the conjecture holds for p ⩽ 2.5 × 10 13 by the aid of computer. And using a result of Bach, we also proved that the conjecture holds for p > 2.5 × 10 13 assuming the extended Riemann Hypothesis. In conclusion, we proved the conjecture is true assuming the extended Riemann Hypothesis.