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Flat knot 6.1673

Min(phi) over symmetries of the knot is: [-2,-1,1,2,0,2,1,0,1,1]
Flat knots (up to 7 crossings) with same phi are :['6.1673']
Arrow polynomial of the knot is: -8*K1**2 - 4*K1*K2 + 2*K1 + 4*K2 + 2*K3 + 5
Flat knots (up to 7 crossings) with same arrow polynomial are :['6.235', '6.379', '6.411', '6.547', '6.811', '6.818', '6.823', '6.897', '6.898', '6.1008', '6.1053', '6.1109', '6.1110', '6.1130', '6.1222', '6.1239', '6.1303', '6.1307', '6.1342', '6.1491', '6.1495', '6.1496', '6.1519', '6.1592', '6.1593', '6.1642', '6.1652', '6.1653', '6.1671', '6.1673', '6.1717']
Outer characteristic polynomial of the knot is: t^5+29t^3+26t
Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1673']
2-strand cable arrow polynomial of the knot is: -320*K1**6 - 192*K1**4*K2**2 + 576*K1**4*K2 - 1792*K1**4 + 128*K1**3*K2*K3 - 1488*K1**2*K2**2 + 2656*K1**2*K2 - 576*K1**2*K3**2 - 112*K1**2*K4**2 - 972*K1**2 + 2168*K1*K2*K3 + 704*K1*K3*K4 + 88*K1*K4*K5 - 256*K2**4 - 208*K2**2*K3**2 - 48*K2**2*K4**2 + 296*K2**2*K4 - 1204*K2**2 + 152*K2*K3*K5 + 32*K2*K4*K6 - 772*K3**2 - 276*K4**2 - 40*K5**2 - 4*K6**2 + 1458
Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1673']
Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.4129', 'vk6.4162', 'vk6.5367', 'vk6.5400', 'vk6.7497', 'vk6.7526', 'vk6.8998', 'vk6.9031', 'vk6.12423', 'vk6.12454', 'vk6.13347', 'vk6.13570', 'vk6.13603', 'vk6.14271', 'vk6.14718', 'vk6.14742', 'vk6.15197', 'vk6.15874', 'vk6.15898', 'vk6.30828', 'vk6.30859', 'vk6.32012', 'vk6.32043', 'vk6.33063', 'vk6.33096', 'vk6.33856', 'vk6.34315', 'vk6.48477', 'vk6.50262', 'vk6.53519', 'vk6.53945', 'vk6.54275']
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 O1O2O3U2O4U5U3U6O5O6U1U4
R3 orbit {'O1O2O3U2O4U5U3U6O5O6U1U4'}
R3 orbit length 1
Gauss code of -K O1O2O3U4U3O5O6U5U1U6O4U2
Gauss code of K* O1O2O3U1U3O4O5U4U6U2O6U5
Gauss code of -K* O1O2O3U4O5U2U5U6O4O6U1U3
Diagrammatic symmetry type c
Flat genus of the diagram 2
If K is checkerboard colorable False
If K is almost classical False
Based matrix from Gauss code [[ 0 -1 -1 1 2 -2 1],[ 1 0 -1 2 2 -1 2],[ 1 1 0 1 1 0 1],[-1 -2 -1 0 0 -1 0],[-2 -2 -1 0 0 -3 -1],[ 2 1 0 1 3 0 2],[-1 -2 -1 0 1 -2 0]]
Primitive based matrix [[ 0 2 1 -1 -2],[-2 0 0 -2 -3],[-1 0 0 -2 -1],[ 1 2 2 0 -1],[ 2 3 1 1 0]]
If based matrix primitive False
Phi of primitive based matrix [-2,-1,1,2,0,2,3,2,1,1]
Phi over symmetry [-2,-1,1,2,0,2,1,0,1,1]
Phi of -K [-2,-1,1,2,0,2,1,0,1,1]
Phi of K* [-2,-1,1,2,1,1,1,0,2,0]
Phi of -K* [-2,-1,1,2,1,1,3,2,2,0]
Symmetry type of based matrix c
u-polynomial 0
Normalized Jones-Krushkal polynomial 13z+27
Enhanced Jones-Krushkal polynomial 13w^2z+27w
Inner characteristic polynomial t^4+19t^2+16
Outer characteristic polynomial t^5+29t^3+26t
Flat arrow polynomial -8*K1**2 - 4*K1*K2 + 2*K1 + 4*K2 + 2*K3 + 5
2-strand cable arrow polynomial -320*K1**6 - 192*K1**4*K2**2 + 576*K1**4*K2 - 1792*K1**4 + 128*K1**3*K2*K3 - 1488*K1**2*K2**2 + 2656*K1**2*K2 - 576*K1**2*K3**2 - 112*K1**2*K4**2 - 972*K1**2 + 2168*K1*K2*K3 + 704*K1*K3*K4 + 88*K1*K4*K5 - 256*K2**4 - 208*K2**2*K3**2 - 48*K2**2*K4**2 + 296*K2**2*K4 - 1204*K2**2 + 152*K2*K3*K5 + 32*K2*K4*K6 - 772*K3**2 - 276*K4**2 - 40*K5**2 - 4*K6**2 + 1458
Genus of based matrix 0
Fillings of based matrix [[{1, 6}, {4, 5}, {2, 3}], [{2, 6}, {4, 5}, {1, 3}]]
If K is slice True
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