Let $A$ and $B$ be two isogenous abelian varieties over a number field $K$ and let $\mathcal{A}$ and $\mathcal{B}$ denote their Neron models over $\mathcal{O}_K$. Let $v \in M_K^0$ denote a finite prime of $K$, $k_v$ its residue field, $\mathcal{A}_v = \mathcal{A} \times _{\mathcal{O}_K} k_v$ the special fiber of the reduction of $A$ at $v$, and $\mathcal{A}_v^0$ the connected component of the identity section in the special fiber $\mathcal{A}_v$.

Is it true that the cardinality of the $k_v$-rational points of $\mathcal{A}_v^0$ and $\mathcal{B}_v^0$ are the same, i.e.

$|\mathcal{A}_v^0(k_v)| = |\mathcal{B}_v^0(k_v)| ,\ \forall v \in M_K^0$?

Let $A$ and $B$ be two isogenous abelian varieties over a number field $K$ and let $\mathcal{A}$ and $\mathcal{B}$ denote their Neron models over $\mathcal{O}_K$. Let $v \in M_K^0$ denote a finite prime of $K$, $k_v$ its residue field, $\mathcal{A}_v = \mathcal{A} \times _{\mathcal{O}_K} k_v$ the special fiber of the reduction of $A$ at $v$, and $\mathcal{A}_v^0$ the connected component of the identity section in the special fiber $\mathcal{A}_v$.

Is it true that the cardinalities of the $k_v$-rational points of $\mathcal{A}_v^0$ and $\mathcal{B}_v^0$ are the same, i.e.

$|\mathcal{A}_v^0(k_v)| = |\mathcal{B}_v^0(k_v)| ,\ \forall v \in M_K^0$?