Let $\phi:E_1\rightarrow E_2$ be an isogeny of elliptic curves. Then $\phi$ induces maps $\phi:E_1[l^n]\rightarrow E_2[l^n]$, and hence induces a $\mathbb{Z}_l$-linear map $\phi_l:T_l(E_1)\rightarrow T_l(E_2)$.
$\mathbb{Z}_l$-linear map are also seen as $\mathbb{Z}$-linear map(because $\mathbb{Z}$ is subring of $\mathbb{Z}_l$), then I believe all entries of representation matrix of $\phi_l$ is in $\mathbb{Z}$.
Is the result (all entries of representation matrix of $\phi_l$ is in $\mathbb{Z}$) and reasoning correct?
P.S Reaction to comments.
・Here, $Tl(Ej)$ means $l$-adic Tate module of elliptic curve $Ej$, that is, inverse lim of $p^n$-torison points of elliptic curve.
・This question's goal is to prove that 'We can find basis whose representation matrix has all entries in Z'. So I don't know how to take the basis, and maybe there are no way to take such a basis. Firstly, I would like to clarify that is possible or not, if possible, I want the example of such a basis, if not possible, I want to prove we cannot take such a basis.