# L11a247

## Contents (Knotscape image) See the full Thistlethwaite Link Table (up to 11 crossings). Visit L11a247 at Knotilus!

### Polynomial invariants

 Multivariable Alexander Polynomial (in $u$, $v$, $w$, ...) $-\frac{(u-1)^3 (v-1)^3}{u^{3/2} v^{3/2}}$ (db) Jones polynomial $-q^{13/2}+4 q^{11/2}-8 q^{9/2}+13 q^{7/2}-18 q^{5/2}+20 q^{3/2}-21 \sqrt{q}+\frac{17}{\sqrt{q}}-\frac{13}{q^{3/2}}+\frac{8}{q^{5/2}}-\frac{4}{q^{7/2}}+\frac{1}{q^{9/2}}$ (db) Signature 1 (db) HOMFLY-PT polynomial $-z^7 a^{-1} +2 a z^5-4 z^5 a^{-1} +2 z^5 a^{-3} -a^3 z^3+5 a z^3-8 z^3 a^{-1} +5 z^3 a^{-3} -z^3 a^{-5} -a^3 z+4 a z-6 z a^{-1} +4 z a^{-3} -z a^{-5} +a z^{-1} - a^{-1} z^{-1}$ (db) Kauffman polynomial $z^5 a^{-7} -z^3 a^{-7} +4 z^6 a^{-6} -6 z^4 a^{-6} +2 z^2 a^{-6} +7 z^7 a^{-5} -11 z^5 a^{-5} +6 z^3 a^{-5} -2 z a^{-5} +7 z^8 a^{-4} +a^4 z^6-6 z^6 a^{-4} -2 a^4 z^4-3 z^4 a^{-4} +a^4 z^2+3 z^2 a^{-4} +4 z^9 a^{-3} +4 a^3 z^7+8 z^7 a^{-3} -10 a^3 z^5-28 z^5 a^{-3} +7 a^3 z^3+25 z^3 a^{-3} -2 a^3 z-8 z a^{-3} +z^{10} a^{-2} +6 a^2 z^8+15 z^8 a^{-2} -13 a^2 z^6-32 z^6 a^{-2} +6 a^2 z^4+20 z^4 a^{-2} -2 z^2 a^{-2} +4 a z^9+8 z^9 a^{-1} +2 a z^7-z^7 a^{-1} -24 a z^5-30 z^5 a^{-1} +24 a z^3+35 z^3 a^{-1} -8 a z-12 z a^{-1} +a z^{-1} + a^{-1} z^{-1} +z^{10}+14 z^8-36 z^6+25 z^4-4 z^2-1$ (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
14           11
12          3 -3
10         51 4
8        83  -5
6       105   5
4      108    -2
2     1110     1
0    812      4
-2   59       -4
-4  38        5
-6 15         -4
-8 3          3
-101           -1
Integral Khovanov Homology $\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z}$ $i=0$ $i=2$ $r=-5$ ${\mathbb Z}$ $r=-4$ ${\mathbb Z}^{3}\oplus{\mathbb Z}_2$ ${\mathbb Z}$ $r=-3$ ${\mathbb Z}^{5}\oplus{\mathbb Z}_2^{3}$ ${\mathbb Z}^{3}$ $r=-2$ ${\mathbb Z}^{8}\oplus{\mathbb Z}_2^{5}$ ${\mathbb Z}^{5}$ $r=-1$ ${\mathbb Z}^{9}\oplus{\mathbb Z}_2^{8}$ ${\mathbb Z}^{8}$ $r=0$ ${\mathbb Z}^{12}\oplus{\mathbb Z}_2^{9}$ ${\mathbb Z}^{11}$ $r=1$ ${\mathbb Z}^{10}\oplus{\mathbb Z}_2^{10}$ ${\mathbb Z}^{10}$ $r=2$ ${\mathbb Z}^{8}\oplus{\mathbb Z}_2^{10}$ ${\mathbb Z}^{10}$ $r=3$ ${\mathbb Z}^{5}\oplus{\mathbb Z}_2^{8}$ ${\mathbb Z}^{8}$ $r=4$ ${\mathbb Z}^{3}\oplus{\mathbb Z}_2^{5}$ ${\mathbb Z}^{5}$ $r=5$ ${\mathbb Z}\oplus{\mathbb Z}_2^{3}$ ${\mathbb Z}^{3}$ $r=6$ ${\mathbb Z}_2$ ${\mathbb Z}$

### Computer Talk

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