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Flat knot 6.1815

Min(phi) over symmetries of the knot is: [-1,-1,0,0,1,1,-1,0,0,1,2,-1,0,1,2,1,0,0,0,1,0]
Flat knots (up to 7 crossings) with same phi are :['6.1815']
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+18t^5+30t^3+5t
Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1815']
2-strand cable arrow polynomial of the knot is: -64*K1**6 - 64*K1**4*K2**2 + 2016*K1**4*K2 - 7008*K1**4 + 224*K1**3*K2*K3 - 1024*K1**3*K3 + 512*K1**2*K2**3 - 6208*K1**2*K2**2 - 224*K1**2*K2*K4 + 12896*K1**2*K2 - 160*K1**2*K3**2 - 4980*K1**2 - 416*K1*K2**2*K3 + 5424*K1*K2*K3 + 256*K1*K3*K4 - 464*K2**4 + 424*K2**2*K4 - 4456*K2**2 - 1180*K3**2 - 112*K4**2 + 4606
Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1815']
Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.20016', 'vk6.20068', 'vk6.21288', 'vk6.21350', 'vk6.27063', 'vk6.27133', 'vk6.28768', 'vk6.28822', 'vk6.38464', 'vk6.38534', 'vk6.40653', 'vk6.40731', 'vk6.45344', 'vk6.45434', 'vk6.47113', 'vk6.47176', 'vk6.56831', 'vk6.56873', 'vk6.57965', 'vk6.58011', 'vk6.61345', 'vk6.61403', 'vk6.62521', 'vk6.62560', 'vk6.66551', 'vk6.66581', 'vk6.67340', 'vk6.67372', 'vk6.69193', 'vk6.69233', 'vk6.69944', 'vk6.69974']
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 O1O2O3U4U5O6O5U3U1O4U2U6
R3 orbit {'O1O2O3U4U5O6O5U3U1O4U2U6'}
R3 orbit length 1
Gauss code of -K O1O2O3U4U2O5U3U1O6O4U6U5
Gauss code of K* O1O2U3O4O5U2U4U1O3O6U5U6
Gauss code of -K* O1O2U3O4O5U6U1O6O3U5U2U4
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 -1 1 1],[ 1 0 0 0 0 1 1],[ 0 0 0 1 -1 0 0],[ 0 0 -1 0 0 0 -1],[ 1 0 1 0 0 2 2],[-1 -1 0 0 -2 0 1],[-1 -1 0 1 -2 -1 0]]
Primitive based matrix [[ 0 1 1 0 0 -1 -1],[-1 0 1 0 0 -1 -2],[-1 -1 0 1 0 -1 -2],[ 0 0 -1 0 -1 0 0],[ 0 0 0 1 0 0 -1],[ 1 1 1 0 0 0 0],[ 1 2 2 0 1 0 0]]
If based matrix primitive True
Phi of primitive based matrix [-1,-1,0,0,1,1,-1,0,0,1,2,-1,0,1,2,1,0,0,0,1,0]
Phi over symmetry [-1,-1,0,0,1,1,-1,0,0,1,2,-1,0,1,2,1,0,0,0,1,0]
Phi of -K [-1,-1,0,0,1,1,0,0,1,0,0,1,1,1,1,-1,1,1,1,2,-1]
Phi of K* [-1,-1,0,0,1,1,-1,1,2,0,1,1,1,0,1,1,0,1,1,1,0]
Phi of -K* [-1,-1,0,0,1,1,0,0,0,1,1,0,1,2,2,-1,-1,0,0,0,-1]
Symmetry type of based matrix c
u-polynomial 0
Normalized Jones-Krushkal polynomial z^2+22z+41
Enhanced Jones-Krushkal polynomial w^3z^2+22w^2z+41w
Inner characteristic polynomial t^6+14t^4+16t^2+1
Outer characteristic polynomial t^7+18t^5+30t^3+5t
Flat arrow polynomial -12*K1**2 + 6*K2 + 7
2-strand cable arrow polynomial -64*K1**6 - 64*K1**4*K2**2 + 2016*K1**4*K2 - 7008*K1**4 + 224*K1**3*K2*K3 - 1024*K1**3*K3 + 512*K1**2*K2**3 - 6208*K1**2*K2**2 - 224*K1**2*K2*K4 + 12896*K1**2*K2 - 160*K1**2*K3**2 - 4980*K1**2 - 416*K1*K2**2*K3 + 5424*K1*K2*K3 + 256*K1*K3*K4 - 464*K2**4 + 424*K2**2*K4 - 4456*K2**2 - 1180*K3**2 - 112*K4**2 + 4606
Genus of based matrix 1
Fillings of based matrix [[{1, 6}, {4, 5}, {2, 3}], [{2, 6}, {1, 5}, {3, 4}], [{3, 6}, {1, 5}, {2, 4}], [{3, 6}, {1, 5}, {4}, {2}], [{4, 6}, {1, 5}, {2, 3}], [{4, 6}, {1, 5}, {3}, {2}], [{6}, {1, 5}, {3, 4}, {2}]]
If K is slice False
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