Fix a conductor and a prime $p$. Then
Do the elliptic curves in the same isogeny class after reduction modulo $p$ have the same number of points over the finite field $\mathbb{F}_{p} ?$
Do the elliptic curves belonging to two different isogeny classes corresponding to the fixed conductor, after reduction modulo $p$ have the same number of points over the finite field $\mathbb{F}_{p} ?$