# L11a450

## Contents (Knotscape image) See the full Thistlethwaite Link Table (up to 11 crossings). Visit L11a450 at Knotilus!

### Polynomial invariants

 Multivariable Alexander Polynomial (in $u$, $v$, $w$, ...) $\frac{(v+w-1) (v w-v-w) (u v w-u w+u-v w+v-1)}{\sqrt{u} v^{3/2} w^{3/2}}$ (db) Jones polynomial $-q^8+3 q^7-6 q^6+11 q^5-15 q^4+18 q^3+ q^{-3} -16 q^2-3 q^{-2} +16 q+7 q^{-1} -11$ (db) Signature 2 (db) HOMFLY-PT polynomial $z^6 a^{-2} +z^6 a^{-4} +z^4 a^{-2} +3 z^4 a^{-4} -z^4 a^{-6} -2 z^4+a^2 z^2-2 z^2 a^{-2} +5 z^2 a^{-4} -2 z^2 a^{-6} -3 z^2+a^2-3 a^{-2} +3 a^{-4} - a^{-6} -2 a^{-2} z^{-2} + a^{-4} z^{-2} + z^{-2}$ (db) Kauffman polynomial $z^5 a^{-9} -2 z^3 a^{-9} +3 z^6 a^{-8} -6 z^4 a^{-8} +2 z^2 a^{-8} +5 z^7 a^{-7} -10 z^5 a^{-7} +7 z^3 a^{-7} -2 z a^{-7} +6 z^8 a^{-6} -13 z^6 a^{-6} +15 z^4 a^{-6} -8 z^2 a^{-6} +3 a^{-6} +4 z^9 a^{-5} -2 z^7 a^{-5} -9 z^5 a^{-5} +19 z^3 a^{-5} -7 z a^{-5} +z^{10} a^{-4} +11 z^8 a^{-4} -36 z^6 a^{-4} +52 z^4 a^{-4} -36 z^2 a^{-4} - a^{-4} z^{-2} +11 a^{-4} +7 z^9 a^{-3} -9 z^7 a^{-3} -6 z^5 a^{-3} +19 z^3 a^{-3} -12 z a^{-3} +2 a^{-3} z^{-1} +z^{10} a^{-2} +9 z^8 a^{-2} +a^2 z^6-28 z^6 a^{-2} -3 a^2 z^4+34 z^4 a^{-2} +3 a^2 z^2-29 z^2 a^{-2} -2 a^{-2} z^{-2} -a^2+11 a^{-2} +3 z^9 a^{-1} +3 a z^7+z^7 a^{-1} -8 a z^5-16 z^5 a^{-1} +6 a z^3+15 z^3 a^{-1} -a z-8 z a^{-1} +2 a^{-1} z^{-1} +4 z^8-7 z^6- z^{-2} +3$ (db)

### Khovanov Homology

The coefficients of the monomials $t^rq^j$ are shown, along with their alternating sums $\chi$ (fixed $j$, alternation over $r$).
 \ r \ j \
-4-3-2-101234567χ
17           1-1
15          2 2
13         41 -3
11        72  5
9       95   -4
7      96    3
5     79     2
3    99      0
1   510       5
-1  26        -4
-3 15         4
-5 2          -2
-71           1
Integral Khovanov Homology $\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z}$ $i=1$ $i=3$ $r=-4$ ${\mathbb Z}$ $r=-3$ ${\mathbb Z}^{2}\oplus{\mathbb Z}_2$ ${\mathbb Z}$ $r=-2$ ${\mathbb Z}^{5}\oplus{\mathbb Z}_2^{2}$ ${\mathbb Z}^{2}$ $r=-1$ ${\mathbb Z}^{6}\oplus{\mathbb Z}_2^{5}$ ${\mathbb Z}^{5}$ $r=0$ ${\mathbb Z}^{10}\oplus{\mathbb Z}_2^{6}$ ${\mathbb Z}^{9}$ $r=1$ ${\mathbb Z}^{9}\oplus{\mathbb Z}_2^{7}$ ${\mathbb Z}^{7}$ $r=2$ ${\mathbb Z}^{9}\oplus{\mathbb Z}_2^{9}$ ${\mathbb Z}^{9}$ $r=3$ ${\mathbb Z}^{6}\oplus{\mathbb Z}_2^{9}$ ${\mathbb Z}^{9}$ $r=4$ ${\mathbb Z}^{5}\oplus{\mathbb Z}_2^{6}$ ${\mathbb Z}^{7}$ $r=5$ ${\mathbb Z}^{2}\oplus{\mathbb Z}_2^{4}$ ${\mathbb Z}^{4}$ $r=6$ ${\mathbb Z}\oplus{\mathbb Z}_2^{2}$ ${\mathbb Z}^{2}$ $r=7$ ${\mathbb Z}_2$ ${\mathbb Z}$

### Computer Talk

Much of the above data can be recomputed by Mathematica using the package KnotTheory. See A Sample KnotTheory Session.