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Flat knot 6.1099

Min(phi) over symmetries of the knot is: [-3,-1,0,1,1,2,1,1,1,3,2,0,0,1,1,1,1,0,-1,0,1]
Flat knots (up to 7 crossings) with same phi are :['6.1099']
Arrow polynomial of the knot is: 4*K1**3 - 6*K1**2 - 2*K1*K2 - 2*K1 + 3*K2 + 4
Flat knots (up to 7 crossings) with same arrow polynomial are :['6.573', '6.628', '6.703', '6.704', '6.723', '6.796', '6.1083', '6.1099', '6.1315']
Outer characteristic polynomial of the knot is: t^7+56t^5+85t^3+8t
Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1099']
2-strand cable arrow polynomial of the knot is: -496*K1**4 - 256*K1**2*K2**4 + 2176*K1**2*K2**3 - 6464*K1**2*K2**2 - 416*K1**2*K2*K4 + 6824*K1**2*K2 - 16*K1**2*K3**2 - 4772*K1**2 + 512*K1*K2**3*K3 - 1024*K1*K2**2*K3 - 96*K1*K2*K3*K4 + 5024*K1*K2*K3 + 328*K1*K3*K4 + 8*K1*K4*K5 - 32*K2**6 + 32*K2**4*K4 - 1768*K2**4 - 336*K2**2*K3**2 - 8*K2**2*K4**2 + 1192*K2**2*K4 - 2320*K2**2 + 120*K2*K3*K5 - 1112*K3**2 - 238*K4**2 - 4*K5**2 + 3140
Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1099']
Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.81591', 'vk6.81599', 'vk6.81677', 'vk6.81689', 'vk6.81749', 'vk6.81756', 'vk6.81768', 'vk6.81770', 'vk6.81973', 'vk6.81979', 'vk6.82280', 'vk6.82290', 'vk6.82405', 'vk6.82409', 'vk6.82442', 'vk6.82448', 'vk6.82522', 'vk6.82703', 'vk6.82707', 'vk6.83207', 'vk6.83616', 'vk6.84188', 'vk6.84199', 'vk6.84386', 'vk6.84400', 'vk6.85983', 'vk6.85992', 'vk6.88184', 'vk6.88750', 'vk6.88782', 'vk6.89112', 'vk6.89123']
The R3 orbit of minmal crossing diagrams contains:
The diagrammatic symmetry type of this knot is c.
The reverse -K is
The mirror image K* is
The reversed 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 O1O2O3O4U1U5O6U4U2O5U3U6
R3 orbit {'O1O2O3O4U1U5O6U4U2O5U3U6'}
R3 orbit length 1
Gauss code of -K O1O2O3O4U5U2O6U3U1O5U6U4
Gauss code of K* O1O2U3O4O5U2O6O3U1U5U6U4
Gauss code of -K* O1O2U3O4O5U1O3O6U5U2U4U6
Diagrammatic symmetry type c
Flat genus of the diagram 3
If K is checkerboard colorable False
If K is almost classical False
Based matrix from Gauss code [[ 0 -3 0 1 1 -1 2],[ 3 0 2 3 1 1 3],[ 0 -2 0 0 0 -1 2],[-1 -3 0 0 1 -2 1],[-1 -1 0 -1 0 -1 0],[ 1 -1 1 2 1 0 2],[-2 -3 -2 -1 0 -2 0]]
Primitive based matrix [[ 0 2 1 1 0 -1 -3],[-2 0 0 -1 -2 -2 -3],[-1 0 0 -1 0 -1 -1],[-1 1 1 0 0 -2 -3],[ 0 2 0 0 0 -1 -2],[ 1 2 1 2 1 0 -1],[ 3 3 1 3 2 1 0]]
If based matrix primitive True
Phi of primitive based matrix [-2,-1,-1,0,1,3,0,1,2,2,3,1,0,1,1,0,2,3,1,2,1]
Phi over symmetry [-3,-1,0,1,1,2,1,1,1,3,2,0,0,1,1,1,1,0,-1,0,1]
Phi of -K [-3,-1,0,1,1,2,1,1,1,3,2,0,0,1,1,1,1,0,-1,0,1]
Phi of K* [-2,-1,-1,0,1,3,0,1,0,1,2,1,1,0,1,1,1,3,0,1,1]
Phi of -K* [-3,-1,0,1,1,2,1,2,1,3,3,1,1,2,2,0,0,2,-1,0,1]
Symmetry type of based matrix c
u-polynomial t^3-t^2-t
Normalized Jones-Krushkal polynomial 5z^2+22z+25
Enhanced Jones-Krushkal polynomial 5w^3z^2-4w^3z+26w^2z+25w
Inner characteristic polynomial t^6+40t^4+52t^2
Outer characteristic polynomial t^7+56t^5+85t^3+8t
Flat arrow polynomial 4*K1**3 - 6*K1**2 - 2*K1*K2 - 2*K1 + 3*K2 + 4
2-strand cable arrow polynomial -496*K1**4 - 256*K1**2*K2**4 + 2176*K1**2*K2**3 - 6464*K1**2*K2**2 - 416*K1**2*K2*K4 + 6824*K1**2*K2 - 16*K1**2*K3**2 - 4772*K1**2 + 512*K1*K2**3*K3 - 1024*K1*K2**2*K3 - 96*K1*K2*K3*K4 + 5024*K1*K2*K3 + 328*K1*K3*K4 + 8*K1*K4*K5 - 32*K2**6 + 32*K2**4*K4 - 1768*K2**4 - 336*K2**2*K3**2 - 8*K2**2*K4**2 + 1192*K2**2*K4 - 2320*K2**2 + 120*K2*K3*K5 - 1112*K3**2 - 238*K4**2 - 4*K5**2 + 3140
Genus of based matrix 1
Fillings of based matrix [[{5, 6}, {3, 4}, {1, 2}]]
If K is slice False
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