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Flat knot 6.1402

Min(phi) over symmetries of the knot is: [-2,-1,1,2,-1,1,3,0,1,-1]
Flat knots (up to 7 crossings) with same phi are :['6.788', '6.1402', '7.32890', '7.35309', '7.37095']
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^5+23t^3+2t
Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.788', '6.1402', '7.32890', '7.37095']
2-strand cable arrow polynomial of the knot is: -256*K1**6 - 128*K1**4*K2**2 + 2048*K1**4*K2 - 8960*K1**4 + 256*K1**3*K2*K3 - 1344*K1**3*K3 - 3872*K1**2*K2**2 - 128*K1**2*K2*K4 + 13328*K1**2*K2 - 288*K1**2*K3**2 - 4080*K1**2 + 4160*K1*K2*K3 + 272*K1*K3*K4 - 112*K2**4 + 80*K2**2*K4 - 4384*K2**2 - 1008*K3**2 - 68*K4**2 + 4482
Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1402']
Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.4769', 'vk6.5106', 'vk6.6335', 'vk6.6764', 'vk6.8296', 'vk6.8749', 'vk6.9666', 'vk6.9977', 'vk6.21025', 'vk6.22449', 'vk6.28473', 'vk6.40253', 'vk6.42174', 'vk6.46755', 'vk6.48808', 'vk6.49026', 'vk6.49842', 'vk6.51508', 'vk6.58970', 'vk6.69810']
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 O1O2O3U2O4U3O5U1O6U5U6U4
R3 orbit {'O1O2O3U2O4U3O5U1O6U5U6U4'}
R3 orbit length 1
Gauss code of -K O1O2O3U4U5U6O5U3O6U1O4U2
Gauss code of K* O1O2O3U4U5U6O5U3O6U1O4U2
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 0 2 0 1],[ 2 0 -1 1 3 1 1],[ 1 1 0 1 1 0 0],[ 0 -1 -1 0 1 0 0],[-2 -3 -1 -1 0 -1 1],[ 0 -1 0 0 1 0 1],[-1 -1 0 0 -1 -1 0]]
Primitive based matrix [[ 0 2 1 -1 -2],[-2 0 1 -1 -3],[-1 -1 0 0 -1],[ 1 1 0 0 1],[ 2 3 1 -1 0]]
If based matrix primitive False
Phi of primitive based matrix [-2,-1,1,2,-1,1,3,0,1,-1]
Phi over symmetry [-2,-1,1,2,-1,1,3,0,1,-1]
Phi of -K [-2,-1,1,2,2,2,1,2,2,2]
Phi of K* [-2,-1,1,2,2,2,1,2,2,2]
Phi of -K* [-2,-1,1,2,-1,1,3,0,1,-1]
Symmetry type of based matrix -
u-polynomial 0
Normalized Jones-Krushkal polynomial 21z+43
Enhanced Jones-Krushkal polynomial 21w^2z+43w
Inner characteristic polynomial t^4+13t^2
Outer characteristic polynomial t^5+23t^3+2t
Flat arrow polynomial -12*K1**2 + 6*K2 + 7
2-strand cable arrow polynomial -256*K1**6 - 128*K1**4*K2**2 + 2048*K1**4*K2 - 8960*K1**4 + 256*K1**3*K2*K3 - 1344*K1**3*K3 - 3872*K1**2*K2**2 - 128*K1**2*K2*K4 + 13328*K1**2*K2 - 288*K1**2*K3**2 - 4080*K1**2 + 4160*K1*K2*K3 + 272*K1*K3*K4 - 112*K2**4 + 80*K2**2*K4 - 4384*K2**2 - 1008*K3**2 - 68*K4**2 + 4482
Genus of based matrix 0
Fillings of based matrix [[{2, 6}, {3, 5}, {1, 4}]]
If K is slice True
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