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Flat knot 6.1401

Min(phi) over symmetries of the knot is: [-2,-1,0,0,1,2,-1,0,1,1,3,1,1,0,0,1,0,1,0,1,0]
Flat knots (up to 7 crossings) with same phi are :['6.1401']
Arrow polynomial of the knot is: -16*K1**2 + 8*K2 + 9
Flat knots (up to 7 crossings) with same arrow polynomial are :['6.1244', '6.1401', '6.2079', '6.2084']
Outer characteristic polynomial of the knot is: t^7+27t^5+45t^3+7t
Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1401']
2-strand cable arrow polynomial of the knot is: -256*K1**6 - 64*K1**4*K2**2 + 1600*K1**4*K2 - 6160*K1**4 + 320*K1**3*K2*K3 - 960*K1**3*K3 + 256*K1**2*K2**3 - 6416*K1**2*K2**2 - 288*K1**2*K2*K4 + 13392*K1**2*K2 - 784*K1**2*K3**2 - 6908*K1**2 - 736*K1*K2**2*K3 + 8320*K1*K2*K3 + 1264*K1*K3*K4 - 512*K2**4 + 928*K2**2*K4 - 6056*K2**2 - 2580*K3**2 - 584*K4**2 + 6222
Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1401']
Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.3640', 'vk6.3735', 'vk6.3930', 'vk6.4025', 'vk6.4495', 'vk6.4592', 'vk6.5881', 'vk6.6010', 'vk6.7131', 'vk6.7310', 'vk6.7401', 'vk6.7934', 'vk6.8055', 'vk6.9368', 'vk6.17924', 'vk6.18021', 'vk6.18744', 'vk6.24463', 'vk6.24867', 'vk6.25330', 'vk6.37483', 'vk6.43898', 'vk6.44214', 'vk6.44519', 'vk6.48280', 'vk6.48343', 'vk6.50069', 'vk6.50183', 'vk6.50579', 'vk6.50644', 'vk6.55869', 'vk6.60722']
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 O1O2O3U2O4U1O5U4O6U5U6U3
R3 orbit {'O1O2O3U2O4U1O5U4O6U5U6U3'}
R3 orbit length 1
Gauss code of -K O1O2O3U1U4U5O4U6O5U3O6U2
Gauss code of K* O1O2O3U4U5U3O5U6O4U1O6U2
Gauss code of -K* O1O2O3U2O4U3O5U4O6U1U6U5
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 -2 -1 2 0 0 1],[ 2 0 0 3 1 1 0],[ 1 0 0 1 0 0 0],[-2 -3 -1 0 -1 0 1],[ 0 -1 0 1 0 1 1],[ 0 -1 0 0 -1 0 1],[-1 0 0 -1 -1 -1 0]]
Primitive based matrix [[ 0 2 1 0 0 -1 -2],[-2 0 1 0 -1 -1 -3],[-1 -1 0 -1 -1 0 0],[ 0 0 1 0 -1 0 -1],[ 0 1 1 1 0 0 -1],[ 1 1 0 0 0 0 0],[ 2 3 0 1 1 0 0]]
If based matrix primitive True
Phi of primitive based matrix [-2,-1,0,0,1,2,-1,0,1,1,3,1,1,0,0,1,0,1,0,1,0]
Phi over symmetry [-2,-1,0,0,1,2,-1,0,1,1,3,1,1,0,0,1,0,1,0,1,0]
Phi of -K [-2,-1,0,0,1,2,1,1,1,3,1,1,1,2,2,-1,0,1,0,2,2]
Phi of K* [-2,-1,0,0,1,2,2,1,2,2,1,0,0,2,3,1,1,1,1,1,1]
Phi of -K* [-2,-1,0,0,1,2,0,1,1,0,3,0,0,0,1,-1,1,0,1,1,-1]
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+17t^4+17t^2
Outer characteristic polynomial t^7+27t^5+45t^3+7t
Flat arrow polynomial -16*K1**2 + 8*K2 + 9
2-strand cable arrow polynomial -256*K1**6 - 64*K1**4*K2**2 + 1600*K1**4*K2 - 6160*K1**4 + 320*K1**3*K2*K3 - 960*K1**3*K3 + 256*K1**2*K2**3 - 6416*K1**2*K2**2 - 288*K1**2*K2*K4 + 13392*K1**2*K2 - 784*K1**2*K3**2 - 6908*K1**2 - 736*K1*K2**2*K3 + 8320*K1*K2*K3 + 1264*K1*K3*K4 - 512*K2**4 + 928*K2**2*K4 - 6056*K2**2 - 2580*K3**2 - 584*K4**2 + 6222
Genus of based matrix 1
Fillings of based matrix [[{2, 6}, {4, 5}, {1, 3}]]
If K is slice False
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