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Flat knot 5.5

Min(phi) over symmetries of the knot is: [-4,-1,1,1,3,1,2,4,3,1,2,2,0,1,2]
Flat knots (up to 7 crossings) with same phi are :['5.5']
Arrow polynomial of the knot is: 8*K1**4 - 4*K1**3 - 4*K1**2*K2 - 4*K1**2 + 2*K1*K2 + 2*K1 + 1
Flat knots (up to 7 crossings) with same arrow polynomial are :['5.5', '7.3503', '7.4776', '7.5966', '7.5967', '7.6294', '7.6308', '7.6343', '7.7034', '7.7128', '7.7593', '7.7600', '7.8161', '7.8260', '7.8579', '7.8654', '7.9085', '7.10611', '7.11225', '7.15811', '7.15824', '7.16574']
Outer characteristic polynomial of the knot is: t^6+72t^4+26t^2
Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['5.5']
2-strand cable arrow polynomial of the knot is: 256*K1**2*K2**5 - 832*K1**2*K2**4 + 416*K1**2*K2**3 - 400*K1**2*K2**2 + 408*K1**2*K2 - 432*K1**2 + 128*K1*K2**5*K3 + 352*K1*K2**3*K3 + 328*K1*K2*K3 + 32*K1*K3*K4 + 8*K1*K4*K5 - 128*K2**8 + 128*K2**6*K4 - 288*K2**6 - 128*K2**4*K3**2 - 32*K2**4*K4**2 + 64*K2**4*K4 + 80*K2**4 + 32*K2**3*K3*K5 - 48*K2**2*K3**2 - 8*K2**2*K4**2 + 64*K2**2*K4 - 144*K2**2 + 16*K2*K3*K5 - 128*K3**2 - 36*K4**2 - 8*K5**2 + 298
Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['5.5']
Virtual knots (up to 6 crossings) projecting to this knot are :'vk5.599', 'vk5.601', 'vk5.724', 'vk5.727', 'vk5.1067', 'vk5.1075', 'vk5.1246', 'vk5.1249', 'vk5.1596', 'vk5.1600', 'vk5.1706', 'vk5.1712', 'vk5.1827', 'vk5.1829', 'vk5.1900', 'vk5.1902']
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 O1O2O3O4O5U1U3U4U5U2
R3 orbit {'O1O2O3O4O5U1U3U4U5U2'}
R3 orbit length 1
Gauss code of -K O1O2O3O4O5U4U1U2U3U5
Gauss code of K* O1O2O3O4O5U1U5U2U3U4
Gauss code of -K* O1O2O3O4O5U2U3U4U1U5
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 -4 1 -1 1 3],[ 4 0 4 1 2 3],[-1 -4 0 -2 0 2],[ 1 -1 2 0 1 2],[-1 -2 0 -1 0 1],[-3 -3 -2 -2 -1 0]]
Primitive based matrix [[ 0 3 1 1 -1 -4],[-3 0 -1 -2 -2 -3],[-1 1 0 0 -1 -2],[-1 2 0 0 -2 -4],[ 1 2 1 2 0 -1],[ 4 3 2 4 1 0]]
If based matrix primitive True
Phi of primitive based matrix [-3,-1,-1,1,4,1,2,2,3,0,1,2,2,4,1]
Phi over symmetry [-4,-1,1,1,3,1,2,4,3,1,2,2,0,1,2]
Phi of -K [-4,-1,1,1,3,2,1,3,4,0,1,2,0,0,1]
Phi of K* [-3,-1,-1,1,4,0,1,2,4,0,0,1,1,3,2]
Phi of -K* [-4,-1,1,1,3,1,2,4,3,1,2,2,0,1,2]
Symmetry type of based matrix c
u-polynomial t^4-t^3-t
Normalized Jones-Krushkal polynomial -2z-3
Enhanced Jones-Krushkal polynomial -4w^4z+8w^3z-6w^2z-3w
Inner characteristic polynomial t^5+44t^3
Outer characteristic polynomial t^6+72t^4+26t^2
Flat arrow polynomial 8*K1**4 - 4*K1**3 - 4*K1**2*K2 - 4*K1**2 + 2*K1*K2 + 2*K1 + 1
2-strand cable arrow polynomial 256*K1**2*K2**5 - 832*K1**2*K2**4 + 416*K1**2*K2**3 - 400*K1**2*K2**2 + 408*K1**2*K2 - 432*K1**2 + 128*K1*K2**5*K3 + 352*K1*K2**3*K3 + 328*K1*K2*K3 + 32*K1*K3*K4 + 8*K1*K4*K5 - 128*K2**8 + 128*K2**6*K4 - 288*K2**6 - 128*K2**4*K3**2 - 32*K2**4*K4**2 + 64*K2**4*K4 + 80*K2**4 + 32*K2**3*K3*K5 - 48*K2**2*K3**2 - 8*K2**2*K4**2 + 64*K2**2*K4 - 144*K2**2 + 16*K2*K3*K5 - 128*K3**2 - 36*K4**2 - 8*K5**2 + 298
Genus of based matrix 1
Fillings of based matrix [[{1, 5}, {4}, {2, 3}], [{3, 5}, {4}, {1, 2}], [{4, 5}, {2, 3}, {1}], [{5}, {1, 4}, {2, 3}]]
If K is slice False
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