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Flat knot 6.1688

Min(phi) over symmetries of the knot is: [-2,-1,-1,1,1,2,-1,1,1,2,1,0,0,0,1,0,1,2,0,-1,1]
Flat knots (up to 7 crossings) with same phi are :['6.1688']
Arrow polynomial of the knot is: 8*K1**3 - 4*K1**2 - 4*K1*K2 - 4*K1 + 2*K2 + 3
Flat knots (up to 7 crossings) with same arrow polynomial are :['6.206', '6.236', '6.575', '6.580', '6.613', '6.619', '6.810', '6.819', '6.831', '6.838', '6.957', '6.1018', '6.1028', '6.1046', '6.1073', '6.1279', '6.1507', '6.1532', '6.1556', '6.1639', '6.1688', '6.1924', '6.1931']
Outer characteristic polynomial of the knot is: t^7+52t^5+176t^3
Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1688']
2-strand cable arrow polynomial of the knot is: -128*K1**6 - 512*K1**4*K2**4 + 1536*K1**4*K2**3 - 1920*K1**4*K2**2 + 1600*K1**4*K2 - 1984*K1**4 + 256*K1**3*K2*K3 + 1280*K1**2*K2**5 - 4224*K1**2*K2**4 + 2944*K1**2*K2**3 - 4000*K1**2*K2**2 + 3888*K1**2*K2 - 96*K1**2*K3**2 - 1696*K1**2 + 1600*K1*K2**3*K3 + 1840*K1*K2*K3 + 112*K1*K3*K4 - 704*K2**6 + 128*K2**4*K4 - 560*K2**4 - 160*K2**2*K3**2 - 16*K2**2*K4**2 + 160*K2**2*K4 - 512*K2**2 + 16*K2*K3*K5 - 352*K3**2 - 68*K4**2 + 1570
Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1688']
Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.14095', 'vk6.14294', 'vk6.15523', 'vk6.16017', 'vk6.16265', 'vk6.16272', 'vk6.22579', 'vk6.34052', 'vk6.34103', 'vk6.34490', 'vk6.34527', 'vk6.34554', 'vk6.42259', 'vk6.54068', 'vk6.54289', 'vk6.54524', 'vk6.54550', 'vk6.59009', 'vk6.64526', 'vk6.64620']
The R3 orbit of minmal crossing diagrams contains:
The diagrammatic symmetry type of this knot is -.
The reverse -K is
The mirror image K* is
The fillings (up to the first 10) associated to the algebraic genus:
Or click here to check the fillings

invariant value
Gauss code O1O2O3U4O5U2U3U6O4O6U1U5
R3 orbit {'O1O2O3U4O5U2U3U6O4O6U1U5'}
R3 orbit length 1
Gauss code of -K O1O2O3U4U3O5O6U5U1U2O4U6
Gauss code of K* O1O2O3U4U3O5O6U5U1U2O4U6
Gauss code of -K* Same
Diagrammatic symmetry type -
Flat genus of the diagram 2
If K is checkerboard colorable False
If K is almost classical False
Based matrix from Gauss code [[ 0 -1 -1 1 -2 2 1],[ 1 0 0 2 -2 2 2],[ 1 0 0 1 0 1 2],[-1 -2 -1 0 -1 0 0],[ 2 2 0 1 0 3 2],[-2 -2 -1 0 -3 0 -2],[-1 -2 -2 0 -2 2 0]]
Primitive based matrix [[ 0 2 1 1 -1 -1 -2],[-2 0 0 -2 -1 -2 -3],[-1 0 0 0 -1 -2 -1],[-1 2 0 0 -2 -2 -2],[ 1 1 1 2 0 0 0],[ 1 2 2 2 0 0 -2],[ 2 3 1 2 0 2 0]]
If based matrix primitive True
Phi of primitive based matrix [-2,-1,-1,1,1,2,0,2,1,2,3,0,1,2,1,2,2,2,0,0,2]
Phi over symmetry [-2,-1,-1,1,1,2,-1,1,1,2,1,0,0,0,1,0,1,2,0,-1,1]
Phi of -K [-2,-1,-1,1,1,2,-1,1,1,2,1,0,0,0,1,0,1,2,0,-1,1]
Phi of K* [-2,-1,-1,1,1,2,-1,1,1,2,1,0,0,0,1,0,1,2,0,-1,1]
Phi of -K* [-2,-1,-1,1,1,2,0,2,1,2,3,0,1,2,1,2,2,2,0,0,2]
Symmetry type of based matrix -
u-polynomial 0
Normalized Jones-Krushkal polynomial 8z+17
Enhanced Jones-Krushkal polynomial 4w^4z-12w^3z+16w^2z+17w
Inner characteristic polynomial t^6+40t^4+132t^2
Outer characteristic polynomial t^7+52t^5+176t^3
Flat arrow polynomial 8*K1**3 - 4*K1**2 - 4*K1*K2 - 4*K1 + 2*K2 + 3
2-strand cable arrow polynomial -128*K1**6 - 512*K1**4*K2**4 + 1536*K1**4*K2**3 - 1920*K1**4*K2**2 + 1600*K1**4*K2 - 1984*K1**4 + 256*K1**3*K2*K3 + 1280*K1**2*K2**5 - 4224*K1**2*K2**4 + 2944*K1**2*K2**3 - 4000*K1**2*K2**2 + 3888*K1**2*K2 - 96*K1**2*K3**2 - 1696*K1**2 + 1600*K1*K2**3*K3 + 1840*K1*K2*K3 + 112*K1*K3*K4 - 704*K2**6 + 128*K2**4*K4 - 560*K2**4 - 160*K2**2*K3**2 - 16*K2**2*K4**2 + 160*K2**2*K4 - 512*K2**2 + 16*K2*K3*K5 - 352*K3**2 - 68*K4**2 + 1570
Genus of based matrix 0
Fillings of based matrix [[{1, 6}, {4, 5}, {2, 3}]]
If K is slice True
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