Consider two (primitive) elements $\pi_{i} \in \mathbb{C}$, such that $\pi_{1} = M \pi_{2}$ for $M \in \mathcal{S}_{m}$ with $$\mathcal{S}_{m}:=\Big\{\begin{pmatrix}
A & B \\
0 & D 
\end{pmatrix} \in \mathrm{GL}_{2}(\mathbb{Z}) : AD = m >0,\; 0 \leq B \leq D\Big\}.$$ 
Let $\Lambda_{i} = \mathbb{Z}\pi_{i} + \mathbb{Z}$ denote the corresponding lattice. Does this imply that: 
(a) the elliptic curves that correspond to these lattices are isogenous, and 
(b) the conductor of the order that corresponds to $\pi_{1}$ divides the conductor of the order that corresponds to $\pi_{2}$, which equals det($M$).