What link is this?

Question

Please consider the following link

its corresponding Jones polynomial is

Could you please identify such link as a member of the Thistlethwaite Link Table?

Many thanks.

Answer 1

Using SnapPy, recommended by N. Owad (Are isomorphic the following two links?) and Jim Belk (What knot is this?); I am obtaining the following result.

The link is drawing inside the SnapPy environment as

Now using the commands

N= Manifold()
N.identify()

we obtain the output

[7^2_6(0,0)(0,0), L7a1(0,0)(0,0)]

It is to say the link L7a1 in the Thistlethwaite Link Table.

The Jones polynomial for L7a1 computed using the Mathematica package KnotTheory is

The ratio between the Jones polynomial of the original link and the Jones polynomial of L7a1 is the monomial $q^{-3}$.

Such ratio confirms that the original link is L7a1. Do you agree?

Answer 2

See here http://www.indiana.edu/~linkinfo/results.php?searchmode=0&category%5B%5D=%3C%3D6&category%5B%5D=%3D7&category%5B%5D=%3D8&category%5B%5D=%3D9&category%5B%5D=%3D%2710%27&category%5B%5D=%3D%2711%27&name=%3D1&jones_polynomial=%3D1&startrow=0&rows=4188

for a list of all links up to 11 crossings with their corresponding Jones' polynomial and here http://www.indiana.edu/~linkinfo/descriptions/jones_homfly_kauffman_description/polynomial_defn.html to see the conventions used in determining the actual polynomial (which I am pretty sure are different then your conventions). Linkinfo and knotinfo make pretty short work of these types of questions.