Maximize it!

The maximum of

$\large \log \left(\sqrt{\left(x^5-10 x^3 y^2+5 x y^4+2\right)^2+\left(5 x^4 y-10 x^2 y^3+y^5\right)^2}\right)$

in the closed unit disk can be written as $\log (a)$ for some positive integer $a$ . Find $a$ .

Note that $\log(\cdot)$ above is the natural logarithm ( $\ln(\cdot)$ ).