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Flat knot 6.1995

Min(phi) over symmetries of the knot is: [-1,0,0,0,0,1,0,0,0,0,1,-1,-1,0,1,-1,-1,1,0,0,0]
Flat knots (up to 7 crossings) with same phi are :['6.1995']
Arrow polynomial of the knot is: -12*K1**2 + 6*K2 + 7
Flat knots (up to 7 crossings) with same arrow polynomial are :['6.612', '6.1246', '6.1402', '6.1410', '6.1411', '6.1468', '6.1617', '6.1666', '6.1667', '6.1815', '6.1904', '6.1994', '6.1995', '6.1996', '6.2001', '6.2014', '6.2015', '6.2016', '6.2017', '6.2020', '6.2022']
Outer characteristic polynomial of the knot is: t^7+9t^5+16t^3+4t
Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1995']
2-strand cable arrow polynomial of the knot is: -640*K1**6 - 192*K1**4*K2**2 + 1792*K1**4*K2 - 7840*K1**4 + 320*K1**3*K2*K3 - 480*K1**3*K3 - 4128*K1**2*K2**2 - 96*K1**2*K2*K4 + 11344*K1**2*K2 - 96*K1**2*K3**2 - 2624*K1**2 + 3248*K1*K2*K3 + 48*K1*K3*K4 - 176*K2**4 + 160*K2**2*K4 - 3544*K2**2 - 656*K3**2 - 40*K4**2 + 3598
Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1995']
Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.3641', 'vk6.3738', 'vk6.3927', 'vk6.4024', 'vk6.4494', 'vk6.4589', 'vk6.5876', 'vk6.6003', 'vk6.7134', 'vk6.7307', 'vk6.7400', 'vk6.7925', 'vk6.8044', 'vk6.9355', 'vk6.17918', 'vk6.18015', 'vk6.18749', 'vk6.24453', 'vk6.24870', 'vk6.25331', 'vk6.37496', 'vk6.43888', 'vk6.44225', 'vk6.44528', 'vk6.48281', 'vk6.48346', 'vk6.50072', 'vk6.50182', 'vk6.50586', 'vk6.50649', 'vk6.55879', 'vk6.60709']
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 O1O2U1O3U2O4U3U5O6O5U4U6
R3 orbit {'O1O2U1O3U2O4U3U5O6O5U4U6'}
R3 orbit length 1
Gauss code of -K O1O2U3U4O5O3U5U6O4U1O6U2
Gauss code of K* O1O2U3U2O4O3U5U6O5U1O6U4
Gauss code of -K* O1O2U3O4U2O5U4U5O6O3U1U6
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 -1 0 0 0 1 0],[ 1 0 1 1 0 1 0],[ 0 -1 0 1 1 0 0],[ 0 -1 -1 0 1 0 1],[ 0 0 -1 -1 0 0 0],[-1 -1 0 0 0 0 0],[ 0 0 0 -1 0 0 0]]
Primitive based matrix [[ 0 1 0 0 0 0 -1],[-1 0 0 0 0 0 -1],[ 0 0 0 1 1 0 -1],[ 0 0 -1 0 1 1 -1],[ 0 0 -1 -1 0 0 0],[ 0 0 0 -1 0 0 0],[ 1 1 1 1 0 0 0]]
If based matrix primitive True
Phi of primitive based matrix [-1,0,0,0,0,1,0,0,0,0,1,-1,-1,0,1,-1,-1,1,0,0,0]
Phi over symmetry [-1,0,0,0,0,1,0,0,0,0,1,-1,-1,0,1,-1,-1,1,0,0,0]
Phi of -K [-1,0,0,0,0,1,0,0,1,1,1,-1,-1,0,1,-1,-1,1,0,1,1]
Phi of K* [-1,0,0,0,0,1,1,1,1,1,1,-1,-1,0,1,-1,1,0,0,0,1]
Phi of -K* [-1,0,0,0,0,1,0,0,1,1,1,0,-1,-1,0,-1,0,0,-1,0,0]
Symmetry type of based matrix c
u-polynomial 0
Normalized Jones-Krushkal polynomial 21z+43
Enhanced Jones-Krushkal polynomial 21w^2z+43w
Inner characteristic polynomial t^6+7t^4+6t^2+1
Outer characteristic polynomial t^7+9t^5+16t^3+4t
Flat arrow polynomial -12*K1**2 + 6*K2 + 7
2-strand cable arrow polynomial -640*K1**6 - 192*K1**4*K2**2 + 1792*K1**4*K2 - 7840*K1**4 + 320*K1**3*K2*K3 - 480*K1**3*K3 - 4128*K1**2*K2**2 - 96*K1**2*K2*K4 + 11344*K1**2*K2 - 96*K1**2*K3**2 - 2624*K1**2 + 3248*K1*K2*K3 + 48*K1*K3*K4 - 176*K2**4 + 160*K2**2*K4 - 3544*K2**2 - 656*K3**2 - 40*K4**2 + 3598
Genus of based matrix 1
Fillings of based matrix [[{2, 6}, {1, 5}, {3, 4}], [{2, 6}, {1, 5}, {4}, {3}], [{2, 6}, {3, 5}, {1, 4}], [{2, 6}, {4, 5}, {1, 3}], [{2, 6}, {4, 5}, {3}, {1}], [{2, 6}, {5}, {1, 4}, {3}], [{3, 6}, {1, 5}, {2, 4}], [{3, 6}, {1, 5}, {4}, {2}], [{4, 6}, {1, 5}, {2, 3}], [{6}, {1, 5}, {4}, {2, 3}]]
If K is slice False
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