Libjstl

I have an issue when I try to align different "align" environments. This is my Latex code :

\\documentclass[10pt, a4paper]{article}

\\usepackage[english]{babel}
\\usepackage[english]{isodate}
\\usepackage[T1]{fontenc}
\\usepackage[hidelinks]{hyperref}
\\usepackage[utf8]{inputenc}

\\usepackage{mathtools}
\\usepackage{amsmath}
\\usepackage{amssymb}

\\begin{document}
    \\section{Example}
    \\subsection*{Degree 1}
    \\begin{align*}
        C_1' & = C_1 \\\\
        C_0' & = a_k + C_0
    \\end{align*}

    \\subsection*{Degree 2}
    \\begin{align*}
        C_2' & = C_2 \\\\
        C_1' & = 2 C_2 a_k + C_1 \\\\
        C_0' & = C_2   a_k^2 + C_1   a_k + C_0
    \\end{align*}

    \\subsection*{Degree 3}
    \\begin{align*}
        C_3' & = C_3 \\\\
        C_2' & = 3 C_3 a_k + C_2 \\\\
        C_1' & = 3 C_3 a_k^2 + 2 C_2 a_k + C_1 \\\\
        C_0' & = C_3 a_k^3 + C_2   a_k^2 + C_1   a_k + C_0
    \\end{align*}

    \\subsection*{Degree 4}
    \\begin{align*}
        C_4' & = C_4 \\\\
        C_3' & = 4 C_4 a_k + C_3 \\\\
        C_2' & = 6 C_4 a_k^2 + 3 C_3 a_k + C_2 \\\\
        C_1' & = 4 C_4 a_k^3 + 3 C_3 a_k^2 + 2 C_2 a_k + C_1 \\\\
        C_0' & = C_4 a_k^4 + C_3 a_k^3 + C_2 a_k^2 + C_1 a_k + C_0
    \\end{align*}

    \\subsection*{Degree 5}
    \\begin{align*}
        C_5' & = C_5 \\\\
        C_4' & = 5 C_5 a_k + C_4 \\\\
        C_3' & = 10 C_5 a_k^2 + 4 C_4 a_k + C_3 \\\\
        C_2' & = 10 C_5 a_k^3 + 6 C_4 a_k^2 + 3 C_3 a_k + C_2 \\\\
        C_1' & = 5 C_5 a_k^4 + 4 C_4 a_k^3 + 3 C_3 a_k^2 + 2 C_2 a_k + C_1 \\\\
        C_0' & = C_5 a_k^5 + C_4 a_k^4 + C_3 a_k^3 + C_2 a_k^2 + C_1 a_k + C_0
    \\end{align*}
\\end{document}

And this is the output :

As you can see, equations are not well aligned. I want to align their left side on the same line but by keeping them in the middle of the page (is this clear ?)