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Flat knot 6.2020

Min(phi) over symmetries of the knot is: [-1,0,0,1,0,0,2,-1,0,0]
Flat knots (up to 7 crossings) with same phi are :['4.9', '5.114', '6.2020', '7.44906', '7.45592']
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+7t^3+6t
Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['5.114', '6.2020', '7.44906', '7.45592']
2-strand cable arrow polynomial of the knot is: -384*K1**6 - 384*K1**4*K2**2 + 3264*K1**4*K2 - 7808*K1**4 + 1216*K1**3*K2*K3 - 1664*K1**3*K3 + 1216*K1**2*K2**3 - 9696*K1**2*K2**2 - 896*K1**2*K2*K4 + 14512*K1**2*K2 - 448*K1**2*K3**2 - 4728*K1**2 - 832*K1*K2**2*K3 + 7520*K1*K2*K3 + 400*K1*K3*K4 - 1040*K2**4 + 960*K2**2*K4 - 4424*K2**2 - 1288*K3**2 - 156*K4**2 + 4658
Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.2020']
Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.11570', 'vk6.11911', 'vk6.12918', 'vk6.13225', 'vk6.20961', 'vk6.22378', 'vk6.28429', 'vk6.31355', 'vk6.31764', 'vk6.32517', 'vk6.32918', 'vk6.40144', 'vk6.42151', 'vk6.46656', 'vk6.52352', 'vk6.52619', 'vk6.53487', 'vk6.58944', 'vk6.64483', 'vk6.69786']
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 O1O2U3O4U1O5U6U4O6O3U5U2
R3 orbit {'O1O2U3O4U1O5U6U4O6O3U5U2'}
R3 orbit length 1
Gauss code of -K O1O2U1U3O4O5U6U5O3U2O6U4
Gauss code of K* O1O2U1U3O4O5U6U5O3U2O6U4
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 -1 1 0 1 0 -1],[ 1 0 1 0 1 0 0],[-1 -1 0 0 0 0 -2],[ 0 0 0 0 0 -1 0],[-1 -1 0 0 0 0 -1],[ 0 0 0 1 0 0 0],[ 1 0 2 0 1 0 0]]
Primitive based matrix [[ 0 1 0 0 -1],[-1 0 0 0 -2],[ 0 0 0 1 0],[ 0 0 -1 0 0],[ 1 2 0 0 0]]
If based matrix primitive False
Phi of primitive based matrix [-1,0,0,1,0,0,2,-1,0,0]
Phi over symmetry [-1,0,0,1,0,0,2,-1,0,0]
Phi of -K [-1,0,0,1,1,1,0,-1,1,1]
Phi of K* [-1,0,0,1,1,1,0,-1,1,1]
Phi of -K* [-1,0,0,1,0,0,2,-1,0,0]
Symmetry type of based matrix -
u-polynomial 0
Normalized Jones-Krushkal polynomial 3z^2+24z+37
Enhanced Jones-Krushkal polynomial 3w^3z^2+24w^2z+37w
Inner characteristic polynomial t^4+5t^2+4
Outer characteristic polynomial t^5+7t^3+6t
Flat arrow polynomial -12*K1**2 + 6*K2 + 7
2-strand cable arrow polynomial -384*K1**6 - 384*K1**4*K2**2 + 3264*K1**4*K2 - 7808*K1**4 + 1216*K1**3*K2*K3 - 1664*K1**3*K3 + 1216*K1**2*K2**3 - 9696*K1**2*K2**2 - 896*K1**2*K2*K4 + 14512*K1**2*K2 - 448*K1**2*K3**2 - 4728*K1**2 - 832*K1*K2**2*K3 + 7520*K1*K2*K3 + 400*K1*K3*K4 - 1040*K2**4 + 960*K2**2*K4 - 4424*K2**2 - 1288*K3**2 - 156*K4**2 + 4658
Genus of based matrix 0
Fillings of based matrix [[{2, 6}, {3, 5}, {1, 4}]]
If K is slice True
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