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Flat knot 6.1910

Min(phi) over symmetries of the knot is: [-2,0,0,0,0,2,0,0,0,1,2,-1,-1,-1,1,0,-1,2,0,1,1]
Flat knots (up to 7 crossings) with same phi are :['6.1910']
Arrow polynomial of the knot is: -8*K1**4 + 8*K1**2*K2 - 2*K2**2 + 3
Flat knots (up to 7 crossings) with same arrow polynomial are :['6.1189', '6.1910']
Outer characteristic polynomial of the knot is: t^7+24t^5+95t^3+33t
Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1910']
2-strand cable arrow polynomial of the knot is: -128*K2**8 + 256*K2**6*K4 - 1216*K2**6 - 192*K2**4*K4**2 + 2272*K2**4*K4 - 5216*K2**4 - 576*K2**3*K6 + 64*K2**2*K4**3 - 672*K2**2*K4**2 + 4264*K2**2*K4 + 916*K2**2 + 248*K2*K4*K6 - 8*K4**4 - 864*K4**2 - 20*K6**2 + 870
Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1910']
Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.70472', 'vk6.70487', 'vk6.70529', 'vk6.70607', 'vk6.70650', 'vk6.70676', 'vk6.70761', 'vk6.70846', 'vk6.70936', 'vk6.70963', 'vk6.71006', 'vk6.71112', 'vk6.71166', 'vk6.71181', 'vk6.71244', 'vk6.71302', 'vk6.72394', 'vk6.72409', 'vk6.72744', 'vk6.73058', 'vk6.73615', 'vk6.74395', 'vk6.74926', 'vk6.75400', 'vk6.76494', 'vk6.76687', 'vk6.77739', 'vk6.78367', 'vk6.79435', 'vk6.79948', 'vk6.87181', 'vk6.90137']
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 O1O2O3U1U2U4O5O6O4U3U6U5
R3 orbit {'O1O2O3U1U2U4O5O6O4U3U6U5'}
R3 orbit length 1
Gauss code of -K O1O2O3U1U4U5O6O4O5U3U2U6
Gauss code of K* O1O2O3U4U5U1O4O5O6U3U2U6
Gauss code of -K* O1O2O3U4U2U1O4O5O6U3U5U6
Diagrammatic symmetry type c
Flat genus of the diagram 3
If K is checkerboard colorable True
If K is almost classical False
Based matrix from Gauss code [[ 0 -2 0 0 2 0 0],[ 2 0 1 2 2 1 1],[ 0 -1 0 1 0 1 1],[ 0 -2 -1 0 0 1 0],[-2 -2 0 0 0 -1 0],[ 0 -1 -1 -1 1 0 0],[ 0 -1 -1 0 0 0 0]]
Primitive based matrix [[ 0 2 0 0 0 0 -2],[-2 0 0 0 0 -1 -2],[ 0 0 0 1 1 1 -1],[ 0 0 -1 0 0 1 -2],[ 0 0 -1 0 0 0 -1],[ 0 1 -1 -1 0 0 -1],[ 2 2 1 2 1 1 0]]
If based matrix primitive True
Phi of primitive based matrix [-2,0,0,0,0,2,0,0,0,1,2,-1,-1,-1,1,0,-1,2,0,1,1]
Phi over symmetry [-2,0,0,0,0,2,0,0,0,1,2,-1,-1,-1,1,0,-1,2,0,1,1]
Phi of -K [-2,0,0,0,0,2,0,1,1,1,2,-1,0,1,2,0,1,1,1,2,2]
Phi of K* [-2,0,0,0,0,2,1,2,2,2,2,-1,-1,0,1,-1,0,0,1,1,1]
Phi of -K* [-2,0,0,0,0,2,1,1,1,2,2,-1,0,-1,1,1,1,0,0,0,0]
Symmetry type of based matrix c
u-polynomial 0
Normalized Jones-Krushkal polynomial 3z^3+17z^2+29z+15
Enhanced Jones-Krushkal polynomial 3w^4z^3+17w^3z^2+29w^2z+15
Inner characteristic polynomial t^6+16t^4+39t^2+9
Outer characteristic polynomial t^7+24t^5+95t^3+33t
Flat arrow polynomial -8*K1**4 + 8*K1**2*K2 - 2*K2**2 + 3
2-strand cable arrow polynomial -128*K2**8 + 256*K2**6*K4 - 1216*K2**6 - 192*K2**4*K4**2 + 2272*K2**4*K4 - 5216*K2**4 - 576*K2**3*K6 + 64*K2**2*K4**3 - 672*K2**2*K4**2 + 4264*K2**2*K4 + 916*K2**2 + 248*K2*K4*K6 - 8*K4**4 - 864*K4**2 - 20*K6**2 + 870
Genus of based matrix 1
Fillings of based matrix [[{1, 6}, {2, 5}, {3, 4}], [{1, 6}, {4, 5}, {2, 3}], [{2, 6}, {1, 5}, {3, 4}], [{2, 6}, {3, 5}, {1, 4}], [{2, 6}, {4, 5}, {1, 3}], [{2, 6}, {5}, {1, 4}, {3}], [{3, 6}, {2, 5}, {1, 4}], [{4, 6}, {1, 5}, {2, 3}], [{4, 6}, {2, 5}, {1, 3}], [{5, 6}, {1, 4}, {2, 3}], [{6}, {3, 5}, {1, 4}, {2}]]
If K is slice False
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