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Flat knot 6.1279

Min(phi) over symmetries of the knot is: [-2,-1,-1,1,1,2,0,1,0,2,2,1,1,1,0,1,1,2,-1,0,1]
Flat knots (up to 7 crossings) with same phi are :['6.1279', '7.37184', '7.37237']
Arrow polynomial of the knot is: 8*K1**3 - 4*K1**2 - 4*K1*K2 - 4*K1 + 2*K2 + 3
Flat knots (up to 7 crossings) with same arrow polynomial are :['6.206', '6.236', '6.575', '6.580', '6.613', '6.619', '6.810', '6.819', '6.831', '6.838', '6.957', '6.1018', '6.1028', '6.1046', '6.1073', '6.1279', '6.1507', '6.1532', '6.1556', '6.1639', '6.1688', '6.1924', '6.1931']
Outer characteristic polynomial of the knot is: t^7+32t^5+62t^3+5t
Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1279', '7.37184']
2-strand cable arrow polynomial of the knot is: -2048*K1**4*K2**2 + 3904*K1**4*K2 - 3840*K1**4 + 960*K1**3*K2*K3 - 256*K1**3*K3 - 2688*K1**2*K2**4 + 6400*K1**2*K2**3 + 128*K1**2*K2**2*K4 - 13280*K1**2*K2**2 - 704*K1**2*K2*K4 + 6640*K1**2*K2 - 208*K1**2 + 2176*K1*K2**3*K3 - 2304*K1*K2**2*K3 - 320*K1*K2**2*K5 + 5968*K1*K2*K3 + 80*K1*K3*K4 - 704*K2**6 + 384*K2**4*K4 - 3760*K2**4 - 224*K2**2*K3**2 - 16*K2**2*K4**2 + 2304*K2**2*K4 + 624*K2**2 + 32*K2*K3*K5 - 416*K3**2 - 100*K4**2 + 1266
Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1279']
Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.306', 'vk6.343', 'vk6.692', 'vk6.740', 'vk6.1480', 'vk6.1936', 'vk6.1973', 'vk6.2456', 'vk6.2639', 'vk6.3107', 'vk6.18261', 'vk6.18598', 'vk6.24745', 'vk6.25153', 'vk6.36870', 'vk6.37333', 'vk6.44092', 'vk6.56064', 'vk6.60619', 'vk6.65731']
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 O1O2O3U1O4O5U4U5O6U2U3U6
R3 orbit {'O1O2O3U1O4O5U4U5O6U2U3U6'}
R3 orbit length 1
Gauss code of -K O1O2O3U4U1U2O4U5U6O5O6U3
Gauss code of K* O1O2O3U4U1U2O4U5U6O5O6U3
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 -1 1 -1 1 2],[ 2 0 1 2 0 0 2],[ 1 -1 0 1 -1 1 2],[-1 -2 -1 0 -1 1 1],[ 1 0 1 1 0 1 0],[-1 0 -1 -1 -1 0 0],[-2 -2 -2 -1 0 0 0]]
Primitive based matrix [[ 0 2 1 1 -1 -1 -2],[-2 0 0 -1 0 -2 -2],[-1 0 0 -1 -1 -1 0],[-1 1 1 0 -1 -1 -2],[ 1 0 1 1 0 1 0],[ 1 2 1 1 -1 0 -1],[ 2 2 0 2 0 1 0]]
If based matrix primitive True
Phi of primitive based matrix [-2,-1,-1,1,1,2,0,1,0,2,2,1,1,1,0,1,1,2,-1,0,1]
Phi over symmetry [-2,-1,-1,1,1,2,0,1,0,2,2,1,1,1,0,1,1,2,-1,0,1]
Phi of -K [-2,-1,-1,1,1,2,0,1,1,3,2,1,1,1,1,1,1,3,-1,0,1]
Phi of K* [-2,-1,-1,1,1,2,0,1,1,3,2,1,1,1,1,1,1,3,-1,0,1]
Phi of -K* [-2,-1,-1,1,1,2,0,1,0,2,2,1,1,1,0,1,1,2,-1,0,1]
Symmetry type of based matrix -
u-polynomial 0
Normalized Jones-Krushkal polynomial 7z^2+24z+21
Enhanced Jones-Krushkal polynomial 7w^3z^2+24w^2z+21w
Inner characteristic polynomial t^6+20t^4+36t^2+1
Outer characteristic polynomial t^7+32t^5+62t^3+5t
Flat arrow polynomial 8*K1**3 - 4*K1**2 - 4*K1*K2 - 4*K1 + 2*K2 + 3
2-strand cable arrow polynomial -2048*K1**4*K2**2 + 3904*K1**4*K2 - 3840*K1**4 + 960*K1**3*K2*K3 - 256*K1**3*K3 - 2688*K1**2*K2**4 + 6400*K1**2*K2**3 + 128*K1**2*K2**2*K4 - 13280*K1**2*K2**2 - 704*K1**2*K2*K4 + 6640*K1**2*K2 - 208*K1**2 + 2176*K1*K2**3*K3 - 2304*K1*K2**2*K3 - 320*K1*K2**2*K5 + 5968*K1*K2*K3 + 80*K1*K3*K4 - 704*K2**6 + 384*K2**4*K4 - 3760*K2**4 - 224*K2**2*K3**2 - 16*K2**2*K4**2 + 2304*K2**2*K4 + 624*K2**2 + 32*K2*K3*K5 - 416*K3**2 - 100*K4**2 + 1266
Genus of based matrix 0
Fillings of based matrix [[{1, 6}, {4, 5}, {2, 3}]]
If K is slice True
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