# L11a400

 (Knotscape image) See the full Thistlethwaite Link Table (up to 11 crossings). Visit L11a400 at Knotilus!

 Planar diagram presentation X6172 X12,6,13,5 X8493 X2,14,3,13 X14,7,15,8 X18,12,19,11 X20,9,21,10 X10,19,5,20 X4,15,1,16 X22,18,11,17 X16,22,17,21 Gauss code {1, -4, 3, -9}, {2, -1, 5, -3, 7, -8}, {6, -2, 4, -5, 9, -11, 10, -6, 8, -7, 11, -10}

### Polynomial invariants

 Multivariable Alexander Polynomial (in ${\displaystyle u}$, ${\displaystyle v}$, ${\displaystyle w}$, ...) ${\displaystyle -{\frac {(u-1)(v-1)^{2}(w-1)^{2}\left(w^{2}+1\right)}{{\sqrt {u}}vw^{2}}}}$ (db) Jones polynomial ${\displaystyle q^{7}-4q^{6}+8q^{5}-14q^{4}+18q^{3}-20q^{2}+21q-16+14q^{-1}-7q^{-2}+4q^{-3}-q^{-4}}$ (db) Signature 2 (db) HOMFLY-PT polynomial ${\displaystyle -z^{8}a^{-2}-5z^{6}a^{-2}+z^{6}a^{-4}+2z^{6}-a^{2}z^{4}-9z^{4}a^{-2}+3z^{4}a^{-4}+7z^{4}-2a^{2}z^{2}-5z^{2}a^{-2}+2z^{2}a^{-4}+5z^{2}+a^{2}+4a^{-2}-a^{-4}-4+2a^{2}z^{-2}+4a^{-2}z^{-2}-a^{-4}z^{-2}-5z^{-2}}$ (db) Kauffman polynomial ${\displaystyle 2z^{10}a^{-2}+2z^{10}+5az^{9}+13z^{9}a^{-1}+8z^{9}a^{-3}+4a^{2}z^{8}+18z^{8}a^{-2}+13z^{8}a^{-4}+9z^{8}+a^{3}z^{7}-14az^{7}-32z^{7}a^{-1}-5z^{7}a^{-3}+12z^{7}a^{-5}-15a^{2}z^{6}-67z^{6}a^{-2}-24z^{6}a^{-4}+8z^{6}a^{-6}-50z^{6}-3a^{3}z^{5}+7az^{5}+11z^{5}a^{-1}-19z^{5}a^{-3}-16z^{5}a^{-5}+4z^{5}a^{-7}+18a^{2}z^{4}+68z^{4}a^{-2}+18z^{4}a^{-4}-6z^{4}a^{-6}+z^{4}a^{-8}+61z^{4}+2a^{3}z^{3}+az^{3}+6z^{3}a^{-1}+15z^{3}a^{-3}+6z^{3}a^{-5}-2z^{3}a^{-7}-7a^{2}z^{2}-24z^{2}a^{-2}-8z^{2}a^{-4}-23z^{2}+5az+9za^{-1}+5za^{-3}+za^{-5}-3a^{2}-2a^{-2}-4-5az^{-1}-9a^{-1}z^{-1}-5a^{-3}z^{-1}-a^{-5}z^{-1}+2a^{2}z^{-2}+4a^{-2}z^{-2}+a^{-4}z^{-2}+5z^{-2}}$ (db)

### Khovanov Homology

The coefficients of the monomials ${\displaystyle t^{r}q^{j}}$ are shown, along with their alternating sums ${\displaystyle \chi }$ (fixed ${\displaystyle j}$, alternation over ${\displaystyle r}$).
 \ r \ j \
-5-4-3-2-10123456χ
15           11
13          3 -3
11         51 4
9        93  -6
7       95   4
5      119    -2
3     109     1
1    813      5
-1   68       -2
-3  310        7
-5 14         -3
-7 3          3
-91           -1
Integral Khovanov Homology
 ${\displaystyle \dim {\mathcal {G}}_{2r+i}\operatorname {KH} _{\mathbb {Z} }^{r}}$ ${\displaystyle i=1}$ ${\displaystyle i=3}$ ${\displaystyle r=-5}$ ${\displaystyle {\mathbb {Z} }}$ ${\displaystyle r=-4}$ ${\displaystyle {\mathbb {Z} }^{3}\oplus {\mathbb {Z} }_{2}}$ ${\displaystyle {\mathbb {Z} }}$ ${\displaystyle r=-3}$ ${\displaystyle {\mathbb {Z} }^{4}\oplus {\mathbb {Z} }_{2}^{3}}$ ${\displaystyle {\mathbb {Z} }^{3}}$ ${\displaystyle r=-2}$ ${\displaystyle {\mathbb {Z} }^{10}\oplus {\mathbb {Z} }_{2}^{4}}$ ${\displaystyle {\mathbb {Z} }^{6}}$ ${\displaystyle r=-1}$ ${\displaystyle {\mathbb {Z} }^{8}\oplus {\mathbb {Z} }_{2}^{8}}$ ${\displaystyle {\mathbb {Z} }^{8}}$ ${\displaystyle r=0}$ ${\displaystyle {\mathbb {Z} }^{13}\oplus {\mathbb {Z} }_{2}^{8}}$ ${\displaystyle {\mathbb {Z} }^{10}}$ ${\displaystyle r=1}$ ${\displaystyle {\mathbb {Z} }^{9}\oplus {\mathbb {Z} }_{2}^{11}}$ ${\displaystyle {\mathbb {Z} }^{11}}$ ${\displaystyle r=2}$ ${\displaystyle {\mathbb {Z} }^{9}\oplus {\mathbb {Z} }_{2}^{9}}$ ${\displaystyle {\mathbb {Z} }^{9}}$ ${\displaystyle r=3}$ ${\displaystyle {\mathbb {Z} }^{5}\oplus {\mathbb {Z} }_{2}^{9}}$ ${\displaystyle {\mathbb {Z} }^{9}}$ ${\displaystyle r=4}$ ${\displaystyle {\mathbb {Z} }^{3}\oplus {\mathbb {Z} }_{2}^{5}}$ ${\displaystyle {\mathbb {Z} }^{5}}$ ${\displaystyle r=5}$ ${\displaystyle {\mathbb {Z} }\oplus {\mathbb {Z} }_{2}^{3}}$ ${\displaystyle {\mathbb {Z} }^{3}}$ ${\displaystyle r=6}$ ${\displaystyle {\mathbb {Z} }_{2}}$ ${\displaystyle {\mathbb {Z} }}$

### Computer Talk

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