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Flat knot 6.1857

Min(phi) over symmetries of the knot is: [-2,-1,0,0,1,2,0,1,2,1,1,1,1,0,1,0,1,2,1,1,0]
Flat knots (up to 7 crossings) with same phi are :['6.1857']
Arrow polynomial of the knot is: -12*K1**2 - 4*K1*K2 + 2*K1 + 6*K2 + 2*K3 + 7
Flat knots (up to 7 crossings) with same arrow polynomial are :['6.546', '6.591', '6.598', '6.666', '6.680', '6.742', '6.778', '6.805', '6.822', '6.824', '6.1129', '6.1512', '6.1647', '6.1678', '6.1705', '6.1847', '6.1857']
Outer characteristic polynomial of the knot is: t^7+35t^5+44t^3+8t
Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1857']
2-strand cable arrow polynomial of the knot is: -384*K1**4*K2**2 + 1152*K1**4*K2 - 5568*K1**4 + 960*K1**3*K2*K3 - 896*K1**3*K3 + 256*K1**2*K2**2*K4 - 6304*K1**2*K2**2 - 1024*K1**2*K2*K4 + 12512*K1**2*K2 - 768*K1**2*K3**2 - 128*K1**2*K4**2 - 32*K1**2*K5**2 - 6928*K1**2 - 832*K1*K2**2*K3 - 320*K1*K2**2*K5 - 256*K1*K2*K3*K4 + 9168*K1*K2*K3 + 1872*K1*K3*K4 + 448*K1*K4*K5 + 80*K1*K5*K6 - 752*K2**4 - 160*K2**2*K3**2 - 16*K2**2*K4**2 + 2032*K2**2*K4 - 6724*K2**2 + 624*K2*K3*K5 + 32*K2*K4*K6 - 3096*K3**2 - 1284*K4**2 - 376*K5**2 - 44*K6**2 + 6754
Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1857']
Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.3570', 'vk6.3594', 'vk6.3815', 'vk6.3848', 'vk6.6989', 'vk6.7022', 'vk6.7207', 'vk6.7235', 'vk6.15334', 'vk6.15461', 'vk6.33968', 'vk6.34013', 'vk6.34428', 'vk6.48234', 'vk6.48385', 'vk6.49964', 'vk6.49996', 'vk6.53995', 'vk6.54051', 'vk6.54499']
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 O1O2O3U4U2O4U5O6O5U1U6U3
R3 orbit {'O1O2O3U4U2O4U5O6O5U1U6U3'}
R3 orbit length 1
Gauss code of -K O1O2O3U1U4U3O5O4U5O6U2U6
Gauss code of K* O1O2O3U1U4U3O5O4U5O6U2U6
Gauss code of -K* Same
Diagrammatic symmetry type -
Flat genus of the diagram 3
If K is checkerboard colorable False
If K is almost classical False
Based matrix from Gauss code [[ 0 -2 0 2 -1 1 0],[ 2 0 1 3 1 2 0],[ 0 -1 0 0 0 0 0],[-2 -3 0 0 -2 -1 -1],[ 1 -1 0 2 0 2 0],[-1 -2 0 1 -2 0 0],[ 0 0 0 1 0 0 0]]
Primitive based matrix [[ 0 2 1 0 0 -1 -2],[-2 0 -1 0 -1 -2 -3],[-1 1 0 0 0 -2 -2],[ 0 0 0 0 0 0 -1],[ 0 1 0 0 0 0 0],[ 1 2 2 0 0 0 -1],[ 2 3 2 1 0 1 0]]
If based matrix primitive True
Phi of primitive based matrix [-2,-1,0,0,1,2,1,0,1,2,3,0,0,2,2,0,0,1,0,0,1]
Phi over symmetry [-2,-1,0,0,1,2,0,1,2,1,1,1,1,0,1,0,1,2,1,1,0]
Phi of -K [-2,-1,0,0,1,2,0,1,2,1,1,1,1,0,1,0,1,2,1,1,0]
Phi of K* [-2,-1,0,0,1,2,0,1,2,1,1,1,1,0,1,0,1,2,1,1,0]
Phi of -K* [-2,-1,0,0,1,2,1,0,1,2,3,0,0,2,2,0,0,1,0,0,1]
Symmetry type of based matrix -
u-polynomial 0
Normalized Jones-Krushkal polynomial 21z+43
Enhanced Jones-Krushkal polynomial 21w^2z+43w
Inner characteristic polynomial t^6+25t^4+28t^2+4
Outer characteristic polynomial t^7+35t^5+44t^3+8t
Flat arrow polynomial -12*K1**2 - 4*K1*K2 + 2*K1 + 6*K2 + 2*K3 + 7
2-strand cable arrow polynomial -384*K1**4*K2**2 + 1152*K1**4*K2 - 5568*K1**4 + 960*K1**3*K2*K3 - 896*K1**3*K3 + 256*K1**2*K2**2*K4 - 6304*K1**2*K2**2 - 1024*K1**2*K2*K4 + 12512*K1**2*K2 - 768*K1**2*K3**2 - 128*K1**2*K4**2 - 32*K1**2*K5**2 - 6928*K1**2 - 832*K1*K2**2*K3 - 320*K1*K2**2*K5 - 256*K1*K2*K3*K4 + 9168*K1*K2*K3 + 1872*K1*K3*K4 + 448*K1*K4*K5 + 80*K1*K5*K6 - 752*K2**4 - 160*K2**2*K3**2 - 16*K2**2*K4**2 + 2032*K2**2*K4 - 6724*K2**2 + 624*K2*K3*K5 + 32*K2*K4*K6 - 3096*K3**2 - 1284*K4**2 - 376*K5**2 - 44*K6**2 + 6754
Genus of based matrix 0
Fillings of based matrix [[{2, 6}, {4, 5}, {1, 3}]]
If K is slice True
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