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Flat knot 6.1599

Min(phi) over symmetries of the knot is: [-2,1,1,0,1,0]
Flat knots (up to 7 crossings) with same phi are :['6.1599']
Arrow polynomial of the knot is: -6*K1**2 + 3*K2 + 4
Flat knots (up to 7 crossings) with same arrow polynomial are :['6.689', '6.691', '6.752', '6.754', '6.1106', '6.1116', '6.1126', '6.1335', '6.1379', '6.1386', '6.1409', '6.1415', '6.1417', '6.1418', '6.1421', '6.1422', '6.1428', '6.1431', '6.1432', '6.1435', '6.1443', '6.1445', '6.1446', '6.1447', '6.1454', '6.1455', '6.1460', '6.1462', '6.1464', '6.1466', '6.1472', '6.1474', '6.1475', '6.1501', '6.1516', '6.1518', '6.1566', '6.1570', '6.1590', '6.1599', '6.1602', '6.1603', '6.1604', '6.1605', '6.1614', '6.1615', '6.1625', '6.1628', '6.1730', '6.1780', '6.1883', '6.1885', '6.1888', '6.1890', '6.1941', '6.1943', '6.1945', '6.1948', '6.1961', '6.1963', '6.1966', '6.1967', '6.1971']
Outer characteristic polynomial of the knot is: t^4+7t^2+1
Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1599']
2-strand cable arrow polynomial of the knot is: -128*K1**6 + 1536*K1**4*K2 - 8848*K1**4 + 64*K1**3*K2*K3 - 960*K1**3*K3 - 2080*K1**2*K2**2 - 32*K1**2*K2*K4 + 11488*K1**2*K2 - 144*K1**2*K3**2 - 2888*K1**2 + 2560*K1*K2*K3 + 144*K1*K3*K4 - 24*K2**4 + 40*K2**2*K4 - 3768*K2**2 - 712*K3**2 - 50*K4**2 + 3800
Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1599']
Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.3643', 'vk6.3740', 'vk6.3933', 'vk6.4030', 'vk6.4471', 'vk6.4568', 'vk6.5857', 'vk6.5986', 'vk6.7128', 'vk6.7305', 'vk6.7398', 'vk6.7910', 'vk6.8031', 'vk6.9344', 'vk6.17920', 'vk6.18017', 'vk6.18756', 'vk6.24459', 'vk6.24879', 'vk6.25342', 'vk6.37503', 'vk6.43886', 'vk6.44234', 'vk6.44539', 'vk6.48283', 'vk6.48348', 'vk6.50066', 'vk6.50180', 'vk6.50571', 'vk6.50636', 'vk6.55881', 'vk6.60734']
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 O1O2O3U1O4U3U4O5U2O6U5U6
R3 orbit {'O1O2O3U1O4U3U4O5U2O6U5U6'}
R3 orbit length 1
Gauss code of -K O1O2O3U4U5O4U2O5U6U1O6U3
Gauss code of K* O1O2U3O4U5O3O5U6U4U1O6U2
Gauss code of -K* O1O2U1O3U2O4O5U4O6U5U3U6
Diagrammatic symmetry type c
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 0 0 1 0 1],[ 2 0 2 1 1 1 0],[ 0 -2 0 -1 1 1 1],[ 0 -1 1 0 1 0 0],[-1 -1 -1 -1 0 0 0],[ 0 -1 -1 0 0 0 1],[-1 0 -1 0 0 -1 0]]
Primitive based matrix [[ 0 1 1 -2],[-1 0 0 0],[-1 0 0 -1],[ 2 0 1 0]]
If based matrix primitive False
Phi of primitive based matrix [-1,-1,2,0,0,1]
Phi over symmetry [-2,1,1,0,1,0]
Phi of -K [-2,1,1,2,3,0]
Phi of K* [-1,-1,2,0,2,3]
Phi of -K* [-2,1,1,0,1,0]
Symmetry type of based matrix c
u-polynomial t^2-2t
Normalized Jones-Krushkal polynomial 21z+43
Enhanced Jones-Krushkal polynomial 21w^2z+43w
Inner characteristic polynomial t^3+t
Outer characteristic polynomial t^4+7t^2+1
Flat arrow polynomial -6*K1**2 + 3*K2 + 4
2-strand cable arrow polynomial -128*K1**6 + 1536*K1**4*K2 - 8848*K1**4 + 64*K1**3*K2*K3 - 960*K1**3*K3 - 2080*K1**2*K2**2 - 32*K1**2*K2*K4 + 11488*K1**2*K2 - 144*K1**2*K3**2 - 2888*K1**2 + 2560*K1*K2*K3 + 144*K1*K3*K4 - 24*K2**4 + 40*K2**2*K4 - 3768*K2**2 - 712*K3**2 - 50*K4**2 + 3800
Genus of based matrix 1
Fillings of based matrix [[{1, 6}, {3, 5}, {2, 4}], [{1, 6}, {3, 5}, {4}, {2}], [{2, 6}, {1, 5}, {3, 4}], [{2, 6}, {3, 5}, {1, 4}], [{4, 6}, {3, 5}, {1, 2}], [{4, 6}, {3, 5}, {2}, {1}], [{5, 6}, {2, 4}, {1, 3}], [{6}, {3, 5}, {1, 4}, {2}]]
If K is slice False
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