What are the default settings of addplot in pgfplot?

Consider the following code from PGFPlots Gallery which draws multiple plots with the names of d2, d3, d4, d5 and d6.

documentclass{article}
usepackage{pgfplots}
pgfplotsset{compat=newest}

pagestyle{empty}

begin{document}
begin{tikzpicture}
begin{loglogaxis}[
    xlabel={Degrees of freedom},
    ylabel={$L_2$ Error}
]
addplot coordinates {
    (5,8.312e-02)    (17,2.547e-02)   (49,7.407e-03)
    (129,2.102e-03)  (321,5.874e-04)  (769,1.623e-04)
    (1793,4.442e-05) (4097,1.207e-05) (9217,3.261e-06)
};

addplot coordinates{
    (7,8.472e-02)    (31,3.044e-02)    (111,1.022e-02)
    (351,3.303e-03)  (1023,1.039e-03)  (2815,3.196e-04)
    (7423,9.658e-05) (18943,2.873e-05) (47103,8.437e-06)
};

addplot coordinates{
    (9,7.881e-02)     (49,3.243e-02)    (209,1.232e-02)
    (769,4.454e-03)   (2561,1.551e-03)  (7937,5.236e-04)
    (23297,1.723e-04) (65537,5.545e-05) (178177,1.751e-05)
};

addplot coordinates{
    (11,6.887e-02)    (71,3.177e-02)     (351,1.341e-02)
    (1471,5.334e-03)  (5503,2.027e-03)   (18943,7.415e-04)
    (61183,2.628e-04) (187903,9.063e-05) (553983,3.053e-05)
};

addplot coordinates{
    (13,5.755e-02)     (97,2.925e-02)     (545,1.351e-02)
    (2561,5.842e-03)   (10625,2.397e-03)  (40193,9.414e-04)
    (141569,3.564e-04) (471041,1.308e-04) (1496065,4.670e-05)
};
legend{$d2$,$d3$,$d4$,$d5$,$d6$}
end{loglogaxis}
end{tikzpicture}
end{document}

and the result is:

Now, I want to only have the plot d4. So, I removed the unneeded section as follows:

documentclass{article}
usepackage{pgfplots}
pgfplotsset{compat=newest}

pagestyle{empty}

begin{document}
begin{tikzpicture}
begin{loglogaxis}[
    xlabel={Degrees of freedom},
    ylabel={$L_2$ Error}
]
addplot coordinates{
    (9,7.881e-02)     (49,3.243e-02)    (209,1.232e-02)
    (769,4.454e-03)   (2561,1.551e-03)  (7937,5.236e-04)
    (23297,1.723e-04) (65537,5.545e-05) (178177,1.751e-05)
};
legend{$d4$}
end{loglogaxis}
end{tikzpicture}
end{document}

and here is the result:

As you can see, the final result for d4 in the above figures are different, e.g. d4 is green and blue in the first and second figure respectively. The reason is that in the first figure, d4 is the third plot, while in the second figure, d4 is the first plot. What I need is to have completely same addplot settings for d4 in both figures. More precisely, d4 in the second figure must have same mark options and color as it has in the first figure, e.g. d4 should be also green in the second figure. I tried to manually add mark and color to addplot command like addplot[color=green, mark options={fill=green}, ...], but at the end of the day, I could not get the desired output. So, I am thinking if we can find the default settings of addplot for d4 in the first figure and use them in the second one.

brown!60!black,every mark/.append style={fill=brown!80!black},mark=otimes*black,mark=star

documentclass{article}
usepackage{pgfplots}
pgfplotsset{compat=newest}

pagestyle{empty}

begin{document}
begin{tikzpicture}
begin{loglogaxis}[
    xlabel={Degrees of freedom},
    ylabel={$L_2$ Error}
]

pgfplotsset{cycle list shift=2}
addplot coordinates{
    (9,7.881e-02)     (49,3.243e-02)    (209,1.232e-02)
    (769,4.454e-03)   (2561,1.551e-03)  (7937,5.236e-04)
    (23297,1.723e-04) (65537,5.545e-05) (178177,1.751e-05)
};
legend{$d4$}
end{loglogaxis}
end{tikzpicture}
end{document}