已知双曲线\(\dfrac{{x}^{2}}{{a}^{2}}-\dfrac{{y}^{2}}{{b}^{2}}=1(a>0,b>0)\)过点\((2\sqrt{2},1)\)，且与椭圆\(\dfrac{{x}^{2}}{4}+\dfrac{{y}^{2}}{{m}^{2}}=1\)有相同的顶点，则该双曲线的离心率为\((\quad)\)
A. \(\sqrt{5}\)
B. \(\dfrac{\sqrt{5}}{2}\) C. \(\dfrac{2\sqrt{5}}{5}\) D. \(2\)
