Please consider the following link
I am using SnapPy with the following code
In[1]: LS = Link([[6, 10, 1, 7],[8, 18, 7, 19],[11, 6, 12, 5],[17, 12, 18, 13],[4, 16, 5, 17],[15, 11, 16, 14],[14, 4, 13, 3],[20, 2, 19, 1],[2, 9, 3, 8],[9, 20, 10, 15]])
In[2]: LSI1=LS.exterior()
In[3]: LSI1.volume()
Out[3]: 17.4771408175
In[4]: LSI1.identify()
and the output from SnapPy is
Out[4]: [10^4_17(0,0)(0,0)(0,0)(0,0), L10a169(0,0)(0,0)(0,0)(0,0)]
Then I am concluding that the considered link is L10a169:
which corresponds to the "Japanese family symbol":
The Jones polynomial computed from the PD code is given by
and the Jones polynomial for L10a169 is given by (http://katlas.org/wiki/L10a169)
As we can see the two Jones polynomials only differ by a multiplicative monomial.
The corresponding Khovanov-Poincaré polynomial is given by
The link L10a169 has unlinking number 3, as it can be converted to the trivial link with 4 components by changing the 3 crossings indicated in the following figure (https://arxiv.org/pdf/1701.01386.pdf )
Please could you confirm such identification?
Many thanks.