# L11a144

## Contents (Knotscape image) See the full Thistlethwaite Link Table (up to 11 crossings). Visit L11a144 at Knotilus!

### Polynomial invariants

 Multivariable Alexander Polynomial (in $u$, $v$, $w$, ...) $\frac{2 u^2 v^4-5 u^2 v^3+5 u^2 v^2-2 u^2 v-2 u v^4+7 u v^3-11 u v^2+7 u v-2 u-2 v^3+5 v^2-5 v+2}{u v^2}$ (db) Jones polynomial $3 q^{9/2}-\frac{4}{q^{9/2}}-6 q^{7/2}+\frac{8}{q^{7/2}}+11 q^{5/2}-\frac{13}{q^{5/2}}-15 q^{3/2}+\frac{16}{q^{3/2}}-q^{11/2}+\frac{1}{q^{11/2}}+17 \sqrt{q}-\frac{19}{\sqrt{q}}$ (db) Signature -1 (db) HOMFLY-PT polynomial $a z^7+z^7 a^{-1} -a^3 z^5+3 a z^5+4 z^5 a^{-1} -z^5 a^{-3} -2 a^3 z^3+a z^3+6 z^3 a^{-1} -3 z^3 a^{-3} -3 a z+4 z a^{-1} -2 z a^{-3} +a^3 z^{-1} -a z^{-1}$ (db) Kauffman polynomial $-2 z^{10} a^{-2} -2 z^{10}-6 a z^9-10 z^9 a^{-1} -4 z^9 a^{-3} -10 a^2 z^8-z^8 a^{-2} -3 z^8 a^{-4} -8 z^8-11 a^3 z^7+2 a z^7+28 z^7 a^{-1} +14 z^7 a^{-3} -z^7 a^{-5} -8 a^4 z^6+13 a^2 z^6+18 z^6 a^{-2} +12 z^6 a^{-4} +27 z^6-4 a^5 z^5+15 a^3 z^5+14 a z^5-25 z^5 a^{-1} -16 z^5 a^{-3} +4 z^5 a^{-5} -a^6 z^4+7 a^4 z^4-2 a^2 z^4-22 z^4 a^{-2} -15 z^4 a^{-4} -17 z^4+2 a^5 z^3-7 a^3 z^3-8 a z^3+14 z^3 a^{-1} +9 z^3 a^{-3} -4 z^3 a^{-5} -a^4 z^2-a^2 z^2+9 z^2 a^{-2} +6 z^2 a^{-4} +3 z^2-2 a z-5 z a^{-1} -3 z a^{-3} -a^2+a^3 z^{-1} +a z^{-1}$ (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 \
-5-4-3-2-10123456χ
12           11
10          2 -2
8         41 3
6        72  -5
4       84   4
2      97    -2
0     108     2
-2    710      3
-4   69       -3
-6  38        5
-8 15         -4
-10 3          3
-121           -1
Integral Khovanov Homology $\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z}$ $i=-2$ $i=0$ $r=-5$ ${\mathbb Z}$ $r=-4$ ${\mathbb Z}^{3}\oplus{\mathbb Z}_2$ ${\mathbb Z}$ $r=-3$ ${\mathbb Z}^{5}\oplus{\mathbb Z}_2^{3}$ ${\mathbb Z}^{3}$ $r=-2$ ${\mathbb Z}^{8}\oplus{\mathbb Z}_2^{5}$ ${\mathbb Z}^{6}$ $r=-1$ ${\mathbb Z}^{9}\oplus{\mathbb Z}_2^{7}$ ${\mathbb Z}^{7}$ $r=0$ ${\mathbb Z}^{10}\oplus{\mathbb Z}_2^{9}$ ${\mathbb Z}^{10}$ $r=1$ ${\mathbb Z}^{8}\oplus{\mathbb Z}_2^{9}$ ${\mathbb Z}^{9}$ $r=2$ ${\mathbb Z}^{7}\oplus{\mathbb Z}_2^{8}$ ${\mathbb Z}^{8}$ $r=3$ ${\mathbb Z}^{4}\oplus{\mathbb Z}_2^{7}$ ${\mathbb Z}^{7}$ $r=4$ ${\mathbb Z}^{2}\oplus{\mathbb Z}_2^{4}$ ${\mathbb Z}^{4}$ $r=5$ ${\mathbb Z}\oplus{\mathbb Z}_2^{2}$ ${\mathbb Z}^{2}$ $r=6$ ${\mathbb Z}_2$ ${\mathbb Z}$

### Computer Talk

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