L6a1

(Knotscape image)	See the full Thistlethwaite Link Table (up to 11 crossings). Visit L6a1 at Knotilus!
	[edit L6a1 Quick Notes] L6a1 is $6_{3}^{2}$ in the Rolfsen table of links.

A kolam with two cycles/components[1]	Depiction with two eights interlaced	Mongolian ornament ; the two eights are horizontal
Another one, sum of two L6a1	Another depiction

Planar diagram presentation	X₆₁₇₂ X_10,3,11,4 X_12,8,5,7 X_8,12,9,11 X₂₅₃₆ X_4,9,1,10
Gauss code	{1, -5, 2, -6}, {5, -1, 3, -4, 6, -2, 4, -3}

A Braid Representative

A Morse Link Presentation

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	${\frac {uv-2u-2v+1}{{\sqrt {u}}{\sqrt {v}}}}$ (db)
Jones polynomial	$-{\frac {1}{q^{9/2}}}+{\frac {1}{q^{7/2}}}-{\frac {3}{q^{5/2}}}-q^{3/2}+{\frac {2}{q^{3/2}}}+2{\sqrt {q}}-{\frac {2}{\sqrt {q}}}$ (db)
Signature	-1 (db)
HOMFLY-PT polynomial	$a^{5}z^{-1}-2za^{3}-a^{3}z^{-1}+z^{3}a+za-za^{-1}$ (db)
Kauffman polynomial	$a^{5}z^{3}-2a^{5}z+a^{5}z^{-1}+a^{4}z^{4}-a^{4}+a^{3}z^{5}-a^{3}z+a^{3}z^{-1}+3a^{2}z^{4}-3a^{2}z^{2}+az^{5}+z^{3}a^{-1}-za^{-1}+2z^{4}-3z^{2}$ (db)

The coefficients of the monomials

t^{r}q^{j}

are shown, along with their alternating sums

\chi

(fixed

j

, alternation over

r

).

-4

-3

-2

-1

0

1

2

χ

4

1

2

1

-1

0

1

0

-2

2

0

-4

1

-6

2

-8

1

0

-10

1

$\dim {\mathcal {G}}_{2r+i}\operatorname {KH} _{\mathbb {Z} }^{r}$	$i=-2$	$i=0$
$r=-4$	${\mathbb {Z} }$	${\mathbb {Z} }$
$r=-3$	${\mathbb {Z} }$
$r=-2$	${\mathbb {Z} }^{2}\oplus {\mathbb {Z} }_{2}$	${\mathbb {Z} }$
$r=-1$	${\mathbb {Z} }_{2}^{2}$	${\mathbb {Z} }^{2}$
$r=0$	${\mathbb {Z} }^{2}$	${\mathbb {Z} }$
$r=1$	${\mathbb {Z} }\oplus {\mathbb {Z} }_{2}$	${\mathbb {Z} }$
$r=2$	${\mathbb {Z} }_{2}$	${\mathbb {Z} }$