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Flat knot 6.129

Min(phi) over symmetries of the knot is: [0]
Flat knots (up to 7 crossings) with same phi are :['6.129', '6.899', '6.1258', '7.13893', '7.14277', '7.20990', '7.25000', '7.25725', '7.28256', '7.28266', '7.31466', '7.36145', '7.36268', '7.44910', '7.45069', '7.45098', '7.45148', '7.45357', '7.45690', '7.45856', '7.46147', '7.46161']
Arrow polynomial of the knot is: -8*K1**2 - 4*K1*K2 + 2*K1 - 4*K2**2 + 4*K2 + 2*K3 + 2*K4 + 7
Flat knots (up to 7 crossings) with same arrow polynomial are :['6.129']
Outer characteristic polynomial of the knot is: t^2
Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.129', '6.899', '6.1258', '7.13893', '7.14277', '7.20990', '7.25000', '7.25725', '7.28256', '7.28266', '7.31466', '7.36145', '7.36268', '7.44910', '7.45069', '7.45098', '7.45148', '7.45357', '7.45690', '7.45856', '7.46147', '7.46161']
2-strand cable arrow polynomial of the knot is: -256*K1**4 + 128*K1**2*K2**3 - 1216*K1**2*K2**2 + 2720*K1**2*K2 - 192*K1**2*K3**2 - 640*K1**2*K4**2 - 3296*K1**2 + 1824*K1*K2*K3 + 256*K1*K3*K4**3 + 1664*K1*K3*K4 + 480*K1*K4*K5 + 160*K1*K5*K6 - 160*K2**4 - 48*K2**2*K4**2 + 240*K2**2*K4 - 1828*K2**2 + 288*K2*K3*K5 + 48*K2*K4*K6 - 64*K3**4 - 384*K3**2*K4**2 + 96*K3**2*K6 - 1360*K3**2 + 128*K3*K4*K7 - 176*K4**4 + 32*K4**2*K8 - 656*K4**2 - 336*K5**2 - 124*K6**2 - 4*K8**2 + 2674
Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.129']
Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.72423', 'vk6.72472', 'vk6.72833', 'vk6.72894', 'vk6.74480', 'vk6.75082', 'vk6.76973', 'vk6.77775', 'vk6.77965', 'vk6.79471', 'vk6.79928', 'vk6.80943', 'vk6.87238', 'vk6.89364']
The R3 orbit of minmal crossing diagrams contains:
The diagrammatic symmetry type of this knot is a.
The fillings (up to the first 10) associated to the algebraic genus:
Or click here to check the fillings

invariant value
Gauss code O1O2O3O4O5O6U4U2U6U1U5U3
R3 orbit {'O1O2O3O4O5O6U4U2U6U1U5U3'}
R3 orbit length 1
Gauss code of -K Same
Gauss code of K* Same
Gauss code of -K* Same
Diagrammatic symmetry type a
Flat genus of the diagram 2
If K is checkerboard colorable False
If K is almost classical False
Based matrix from Gauss code [[ 0 -2 -3 2 -2 3 2],[ 2 0 -1 3 -1 3 2],[ 3 1 0 3 0 3 2],[-2 -3 -3 0 -2 1 1],[ 2 1 0 2 0 2 1],[-3 -3 -3 -1 -2 0 0],[-2 -2 -2 -1 -1 0 0]]
Primitive based matrix [[0 0],[0 0]]
If based matrix primitive False
Phi of primitive based matrix [0]
Phi over symmetry [0]
Phi of -K [0]
Phi of K* [0]
Phi of -K* [0]
Symmetry type of based matrix a
u-polynomial 0
Normalized Jones-Krushkal polynomial 12z+25
Enhanced Jones-Krushkal polynomial -2w^3z+14w^2z+25w
Inner characteristic polynomial t
Outer characteristic polynomial t^2
Flat arrow polynomial -8*K1**2 - 4*K1*K2 + 2*K1 - 4*K2**2 + 4*K2 + 2*K3 + 2*K4 + 7
2-strand cable arrow polynomial -256*K1**4 + 128*K1**2*K2**3 - 1216*K1**2*K2**2 + 2720*K1**2*K2 - 192*K1**2*K3**2 - 640*K1**2*K4**2 - 3296*K1**2 + 1824*K1*K2*K3 + 256*K1*K3*K4**3 + 1664*K1*K3*K4 + 480*K1*K4*K5 + 160*K1*K5*K6 - 160*K2**4 - 48*K2**2*K4**2 + 240*K2**2*K4 - 1828*K2**2 + 288*K2*K3*K5 + 48*K2*K4*K6 - 64*K3**4 - 384*K3**2*K4**2 + 96*K3**2*K6 - 1360*K3**2 + 128*K3*K4*K7 - 176*K4**4 + 32*K4**2*K8 - 656*K4**2 - 336*K5**2 - 124*K6**2 - 4*K8**2 + 2674
Genus of based matrix 0
Fillings of based matrix [[{1, 6}, {2, 5}, {3, 4}], [{4, 6}, {2, 5}, {1, 3}]]
If K is slice True
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