Min(phi) over symmetries of the knot is: [-2,-2,-1,1,2,2,0,-1,1,1,2,-1,1,2,3,1,0,1,0,-1,0] |
Flat knots (up to 7 crossings) with same phi are :['6.409', '7.19809'] |
Arrow polynomial of the knot is: 8*K1**3 - 4*K1*K2 - 4*K1 + 1 |
Flat knots (up to 7 crossings) with same arrow polynomial are :['6.134', '6.409', '6.424', '6.534', '6.942', '6.969', '6.1192', '6.1280', '6.1310', '6.1325', '6.1858', '6.1925'] |
Outer characteristic polynomial of the knot is: t^7+43t^5+85t^3+19t |
Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.409', '7.19809'] |
2-strand cable arrow polynomial of the knot is: -640*K1**2*K2**4 + 960*K1**2*K2**3 + 512*K1**2*K2**2*K4 - 5856*K1**2*K2**2 - 384*K1**2*K2*K4 + 4352*K1**2*K2 - 256*K1**2*K4**2 - 2128*K1**2 + 960*K1*K2**3*K3 - 960*K1*K2**2*K3 - 512*K1*K2**2*K5 - 256*K1*K2*K3*K4 + 4160*K1*K2*K3 + 496*K1*K3*K4 + 240*K1*K4*K5 - 960*K2**6 + 1696*K2**4*K4 - 5216*K2**4 - 448*K2**3*K6 - 160*K2**2*K3**2 - 656*K2**2*K4**2 + 3880*K2**2*K4 + 288*K2**2 + 128*K2*K3*K5 + 280*K2*K4*K6 - 624*K3**2 - 600*K4**2 - 32*K5**2 - 16*K6**2 + 1750 |
Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.409'] |
Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.325', 'vk6.362', 'vk6.367', 'vk6.719', 'vk6.764', 'vk6.773', 'vk6.1453', 'vk6.1510', 'vk6.1517', 'vk6.1955', 'vk6.1992', 'vk6.1997', 'vk6.2460', 'vk6.2662', 'vk6.2998', 'vk6.3122', 'vk6.18395', 'vk6.18398', 'vk6.18733', 'vk6.18738', 'vk6.24854', 'vk6.24859', 'vk6.25313', 'vk6.25322', 'vk6.37050', 'vk6.37055', 'vk6.44205', 'vk6.44208', 'vk6.56169', 'vk6.56172', 'vk6.60703', 'vk6.60706'] |
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 | O1O2O3O4O5U4U5O6U2U1U6U3 |
R3 orbit | {'O1O2O3O4O5U4U5O6U2U1U6U3'} |
R3 orbit length | 1 |
Gauss code of -K | O1O2O3O4O5U3U6U5U4O6U1U2 |
Gauss code of K* | O1O2O3O4U2U1U4U5U6O5O6U3 |
Gauss code of -K* | O1O2O3O4U2O5O6U5U6U1U4U3 |
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 -2 2 -1 1 2],[ 2 0 0 3 -1 1 2],[ 2 0 0 2 -1 1 1],[-2 -3 -2 0 -1 1 0],[ 1 1 1 1 0 1 0],[-1 -1 -1 -1 -1 0 0],[-2 -2 -1 0 0 0 0]] |
Primitive based matrix | [[ 0 2 2 1 -1 -2 -2],[-2 0 0 1 -1 -2 -3],[-2 0 0 0 0 -1 -2],[-1 -1 0 0 -1 -1 -1],[ 1 1 0 1 0 1 1],[ 2 2 1 1 -1 0 0],[ 2 3 2 1 -1 0 0]] |
If based matrix primitive | True |
Phi of primitive based matrix | [-2,-2,-1,1,2,2,0,-1,1,2,3,0,0,1,2,1,1,1,-1,-1,0] |
Phi over symmetry | [-2,-2,-1,1,2,2,0,-1,1,1,2,-1,1,2,3,1,0,1,0,-1,0] |
Phi of -K | [-2,-2,-1,1,2,2,0,2,2,1,2,2,2,2,3,1,2,3,2,1,0] |
Phi of K* | [-2,-2,-1,1,2,2,0,1,3,2,3,2,2,1,2,1,2,2,2,2,0] |
Phi of -K* | [-2,-2,-1,1,2,2,0,-1,1,1,2,-1,1,2,3,1,0,1,0,-1,0] |
Symmetry type of based matrix | c |
u-polynomial | 0 |
Normalized Jones-Krushkal polynomial | 3z^2+8z+5 |
Enhanced Jones-Krushkal polynomial | -6w^4z^2+9w^3z^2-16w^3z+24w^2z+5w |
Inner characteristic polynomial | t^6+25t^4+33t^2+1 |
Outer characteristic polynomial | t^7+43t^5+85t^3+19t |
Flat arrow polynomial | 8*K1**3 - 4*K1*K2 - 4*K1 + 1 |
2-strand cable arrow polynomial | -640*K1**2*K2**4 + 960*K1**2*K2**3 + 512*K1**2*K2**2*K4 - 5856*K1**2*K2**2 - 384*K1**2*K2*K4 + 4352*K1**2*K2 - 256*K1**2*K4**2 - 2128*K1**2 + 960*K1*K2**3*K3 - 960*K1*K2**2*K3 - 512*K1*K2**2*K5 - 256*K1*K2*K3*K4 + 4160*K1*K2*K3 + 496*K1*K3*K4 + 240*K1*K4*K5 - 960*K2**6 + 1696*K2**4*K4 - 5216*K2**4 - 448*K2**3*K6 - 160*K2**2*K3**2 - 656*K2**2*K4**2 + 3880*K2**2*K4 + 288*K2**2 + 128*K2*K3*K5 + 280*K2*K4*K6 - 624*K3**2 - 600*K4**2 - 32*K5**2 - 16*K6**2 + 1750 |
Genus of based matrix | 0 |
Fillings of based matrix | [[{2, 6}, {4, 5}, {1, 3}]] |
If K is slice | True |