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Flat knot 6.2043

Min(phi) over symmetries of the knot is: [-1,-1,0,0,1,1,-1,0,2,-1,1,0,0,1,0,-1,2,0,0,0,1]
Flat knots (up to 7 crossings) with same phi are :['6.2043']
Arrow polynomial of the knot is: -8*K1**2 + 4*K2 + 5
Flat knots (up to 7 crossings) with same arrow polynomial are :['6.668', '6.711', '6.777', '6.803', '6.828', '6.1015', '6.1032', '6.1055', '6.1082', '6.1132', '6.1264', '6.1288', '6.1333', '6.1391', '6.1395', '6.1396', '6.1400', '6.1404', '6.1405', '6.1419', '6.1471', '6.1473', '6.1536', '6.1563', '6.1611', '6.1618', '6.1623', '6.1627', '6.1629', '6.1631', '6.1695', '6.1700', '6.1731', '6.1740', '6.1767', '6.1773', '6.1790', '6.1792', '6.1796', '6.1848', '6.1899', '6.1901', '6.1937', '6.1954', '6.1955', '6.1958', '6.1964', '6.1975', '6.1997', '6.1998', '6.1999', '6.2002', '6.2003', '6.2004', '6.2005', '6.2007', '6.2008', '6.2009', '6.2010', '6.2011', '6.2013', '6.2018', '6.2019', '6.2021', '6.2034', '6.2039', '6.2043', '6.2046', '6.2050', '6.2051', '6.2057', '6.2063']
Outer characteristic polynomial of the knot is: t^7+30t^5+199t^3+6t
Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.2043']
2-strand cable arrow polynomial of the knot is: -384*K1**6 - 384*K1**4*K2**2 + 1600*K1**4*K2 - 3520*K1**4 + 1024*K1**3*K2*K3 - 256*K1**3*K3 - 4128*K1**2*K2**2 - 128*K1**2*K2*K4 + 7424*K1**2*K2 - 608*K1**2*K3**2 - 3784*K1**2 - 512*K1*K2**2*K3 + 4592*K1*K2*K3 + 464*K1*K3*K4 - 288*K2**4 + 480*K2**2*K4 - 3568*K2**2 - 1400*K3**2 - 192*K4**2 + 3566
Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.2043']
Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.11560', 'vk6.11901', 'vk6.12913', 'vk6.13219', 'vk6.20970', 'vk6.22388', 'vk6.28436', 'vk6.31349', 'vk6.31761', 'vk6.32515', 'vk6.32916', 'vk6.40147', 'vk6.42153', 'vk6.46658', 'vk6.52333', 'vk6.52597', 'vk6.53473', 'vk6.58955', 'vk6.64475', 'vk6.69791']
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 O1O2U3O4U5U6O3O6U2O5U1U4
R3 orbit {'O1O2U3O4U5U6O3O6U2O5U1U4'}
R3 orbit length 1
Gauss code of -K O1O2U1U3O4U2O5O6U4U6O3U5
Gauss code of K* O1O2U1U3O4U2O5O6U4U6O3U5
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 0 -1 1 0 1],[ 1 0 1 -1 1 1 2],[ 0 -1 0 -1 -1 1 1],[ 1 1 1 0 3 -1 1],[-1 -1 1 -3 0 -1 -1],[ 0 -1 -1 1 1 0 1],[-1 -2 -1 -1 1 -1 0]]
Primitive based matrix [[ 0 1 1 0 0 -1 -1],[-1 0 1 -1 -1 -1 -2],[-1 -1 0 1 -1 -3 -1],[ 0 1 -1 0 1 -1 -1],[ 0 1 1 -1 0 1 -1],[ 1 1 3 1 -1 0 1],[ 1 2 1 1 1 -1 0]]
If based matrix primitive True
Phi of primitive based matrix [-1,-1,0,0,1,1,-1,1,1,1,2,-1,1,3,1,-1,1,1,-1,1,-1]
Phi over symmetry [-1,-1,0,0,1,1,-1,0,2,-1,1,0,0,1,0,-1,2,0,0,0,1]
Phi of -K [-1,-1,0,0,1,1,-1,0,2,-1,1,0,0,1,0,-1,2,0,0,0,1]
Phi of K* [-1,-1,0,0,1,1,-1,0,2,-1,1,0,0,1,0,-1,2,0,0,0,1]
Phi of -K* [-1,-1,0,0,1,1,-1,1,1,1,2,-1,1,3,1,-1,1,1,-1,1,-1]
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^6+26t^4+153t^2+4
Outer characteristic polynomial t^7+30t^5+199t^3+6t
Flat arrow polynomial -8*K1**2 + 4*K2 + 5
2-strand cable arrow polynomial -384*K1**6 - 384*K1**4*K2**2 + 1600*K1**4*K2 - 3520*K1**4 + 1024*K1**3*K2*K3 - 256*K1**3*K3 - 4128*K1**2*K2**2 - 128*K1**2*K2*K4 + 7424*K1**2*K2 - 608*K1**2*K3**2 - 3784*K1**2 - 512*K1*K2**2*K3 + 4592*K1*K2*K3 + 464*K1*K3*K4 - 288*K2**4 + 480*K2**2*K4 - 3568*K2**2 - 1400*K3**2 - 192*K4**2 + 3566
Genus of based matrix 0
Fillings of based matrix [[{1, 6}, {2, 5}, {3, 4}]]
If K is slice True
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