L11a107

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Planar diagram presentation	X₆₁₇₂ X_14,3,15,4 X_22,15,5,16 X_16,7,17,8 X_18,9,19,10 X_20,11,21,12 X_8,17,9,18 X_10,19,11,20 X_12,21,13,22 X₂₅₃₆ X_4,13,1,14
Gauss code	{1, -10, 2, -11}, {10, -1, 4, -7, 5, -8, 6, -9, 11, -2, 3, -4, 7, -5, 8, -6, 9, -3}

A Braid Representative

A Morse Link Presentation

Polynomial invariants

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	${\frac {-t(2)^{7}-2t(1)t(2)^{6}+2t(2)^{6}+2t(1)t(2)^{5}-2t(2)^{5}-2t(1)t(2)^{4}+2t(2)^{4}+2t(1)t(2)^{3}-2t(2)^{3}-2t(1)t(2)^{2}+2t(2)^{2}+2t(1)t(2)-2t(2)-t(1)}{{\sqrt {t(1)}}t(2)^{7/2}}}$ (db)
Jones polynomial	${\frac {2}{q^{9/2}}}-{\frac {1}{q^{7/2}}}+{\frac {1}{q^{29/2}}}-{\frac {2}{q^{27/2}}}+{\frac {4}{q^{25/2}}}-{\frac {5}{q^{23/2}}}+{\frac {7}{q^{21/2}}}-{\frac {8}{q^{19/2}}}+{\frac {7}{q^{17/2}}}-{\frac {7}{q^{15/2}}}+{\frac {4}{q^{13/2}}}-{\frac {4}{q^{11/2}}}$ (db)
Signature	-7 (db)
HOMFLY-PT polynomial	$-z^{3}a^{13}-4za^{13}-3a^{13}z^{-1}+3z^{5}a^{11}+15z^{3}a^{11}+20za^{11}+7a^{11}z^{-1}-2z^{7}a^{9}-12z^{5}a^{9}-23z^{3}a^{9}-17za^{9}-4a^{9}z^{-1}-z^{7}a^{7}-5z^{5}a^{7}-6z^{3}a^{7}-za^{7}$ (db)
Kauffman polynomial	$a^{18}z^{4}-2a^{18}z^{2}+a^{18}+2a^{17}z^{5}-3a^{17}z^{3}+2a^{16}z^{6}-a^{16}z^{4}-2a^{16}z^{2}+2a^{15}z^{7}-2a^{15}z^{5}+a^{15}z^{3}+2a^{14}z^{8}-4a^{14}z^{6}+4a^{14}z^{4}+2a^{13}z^{9}-7a^{13}z^{7}+12a^{13}z^{5}-12a^{13}z^{3}+10a^{13}z-3a^{13}z^{-1}+a^{12}z^{10}-a^{12}z^{8}-9a^{12}z^{6}+24a^{12}z^{4}-22a^{12}z^{2}+7a^{12}+5a^{11}z^{9}-27a^{11}z^{7}+55a^{11}z^{5}-57a^{11}z^{3}+29a^{11}z-7a^{11}z^{-1}+a^{10}z^{10}-a^{10}z^{8}-12a^{10}z^{6}+27a^{10}z^{4}-23a^{10}z^{2}+7a^{10}+3a^{9}z^{9}-17a^{9}z^{7}+34a^{9}z^{5}-35a^{9}z^{3}+18a^{9}z-4a^{9}z^{-1}+2a^{8}z^{8}-9a^{8}z^{6}+9a^{8}z^{4}-a^{8}z^{2}+a^{7}z^{7}-5a^{7}z^{5}+6a^{7}z^{3}-a^{7}z$ (db)

Khovanov Homology

The coefficients of the monomials

t^{r}q^{j}

are shown, along with their alternating sums

\chi

(fixed

j

, alternation over

r

).

\		r
	\
j		\

-11

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

0

χ

-6

1

-8

2

1

-1

-10

2

-12

2

0

-14

5

2

3

-16

3

0

-18

5

4

1

-20

2

3

1

-22

3

5

-2

-24

1

2

1

-26

1

3

-2

-28

1

-30

1

-1

Integral Khovanov Homology

(db, data source)

$\dim {\mathcal {G}}_{2r+i}\operatorname {KH} _{\mathbb {Z} }^{r}$	$i=-8$	$i=-6$
$r=-11$	${\mathbb {Z} }$
$r=-10$	${\mathbb {Z} }\oplus {\mathbb {Z} }_{2}$	${\mathbb {Z} }$
$r=-9$	${\mathbb {Z} }^{3}\oplus {\mathbb {Z} }_{2}$	${\mathbb {Z} }$
$r=-8$	${\mathbb {Z} }^{2}\oplus {\mathbb {Z} }_{2}^{3}$	${\mathbb {Z} }^{3}$
$r=-7$	${\mathbb {Z} }^{5}\oplus {\mathbb {Z} }_{2}^{2}$	${\mathbb {Z} }^{2}$
$r=-6$	${\mathbb {Z} }^{3}\oplus {\mathbb {Z} }_{2}^{5}$	${\mathbb {Z} }^{5}$
$r=-5$	${\mathbb {Z} }^{4}\oplus {\mathbb {Z} }_{2}^{3}$	${\mathbb {Z} }^{3}$
$r=-4$	${\mathbb {Z} }^{3}\oplus {\mathbb {Z} }_{2}^{4}$	${\mathbb {Z} }^{5}$
$r=-3$	${\mathbb {Z} }^{2}\oplus {\mathbb {Z} }_{2}^{2}$	${\mathbb {Z} }^{2}$
$r=-2$	${\mathbb {Z} }^{2}\oplus {\mathbb {Z} }_{2}^{2}$	${\mathbb {Z} }^{2}$
$r=-1$	${\mathbb {Z} }_{2}^{2}$	${\mathbb {Z} }^{2}$
$r=0$	${\mathbb {Z} }$	${\mathbb {Z} }$