| Min(phi) over symmetries of the knot is: [-2,0,0,0,1,1,0,1,1,1,3,0,1,0,1,0,1,0,1,0,-1] |
| Flat knots (up to 7 crossings) with same phi are :['6.1771'] |
| Arrow polynomial of the knot is: -10*K1**2 + 5*K2 + 6 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.947', '6.1027', '6.1399', '6.1430', '6.1433', '6.1442', '6.1465', '6.1469', '6.1476', '6.1505', '6.1529', '6.1606', '6.1612', '6.1613', '6.1616', '6.1649', '6.1694', '6.1736', '6.1768', '6.1771', '6.1774', '6.1884', '6.1886', '6.1887', '6.1889', '6.1960', '6.1962'] |
| Outer characteristic polynomial of the knot is: t^7+23t^5+35t^3+9t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1771'] |
| 2-strand cable arrow polynomial of the knot is: -192*K1**4*K2**2 + 768*K1**4*K2 - 1792*K1**4 + 224*K1**3*K2*K3 - 256*K1**3*K3 + 128*K1**2*K2**3 - 5552*K1**2*K2**2 - 96*K1**2*K2*K4 + 7440*K1**2*K2 - 96*K1**2*K3**2 - 4228*K1**2 - 64*K1*K2**2*K3 + 4560*K1*K2*K3 + 72*K1*K3*K4 - 104*K2**4 + 104*K2**2*K4 - 2944*K2**2 - 916*K3**2 - 30*K4**2 + 2972 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1771'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.11287', 'vk6.11367', 'vk6.12550', 'vk6.12663', 'vk6.18346', 'vk6.18685', 'vk6.24785', 'vk6.25244', 'vk6.30972', 'vk6.31100', 'vk6.32151', 'vk6.32272', 'vk6.36975', 'vk6.37431', 'vk6.44159', 'vk6.44481', 'vk6.52059', 'vk6.52140', 'vk6.52896', 'vk6.52959', 'vk6.56131', 'vk6.56357', 'vk6.60650', 'vk6.60993', 'vk6.63674', 'vk6.63720', 'vk6.64104', 'vk6.64150', 'vk6.65789', 'vk6.66047', 'vk6.68789', 'vk6.68999'] |
| 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 | O1O2O3U4U2O5O4U1U5O6U3U6 |
| R3 orbit | {'O1O2O3U4U2O5O4U1U5O6U3U6'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U4U1O4U5U3O6O5U2U6 |
| Gauss code of K* | O1O2U3O4O3U1U5U4O6O5U2U6 |
| Gauss code of -K* | O1O2U1O3O4U5U3O6O5U2U6U4 |
| 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 1 0 0 1],[ 2 0 1 3 1 0 1],[ 0 -1 0 0 0 -1 1],[-1 -3 0 0 0 -1 1],[ 0 -1 0 0 0 0 1],[ 0 0 1 1 0 0 0],[-1 -1 -1 -1 -1 0 0]] |
| Primitive based matrix | [[ 0 1 1 0 0 0 -2],[-1 0 1 0 0 -1 -3],[-1 -1 0 -1 -1 0 -1],[ 0 0 1 0 0 0 -1],[ 0 0 1 0 0 -1 -1],[ 0 1 0 0 1 0 0],[ 2 3 1 1 1 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-1,-1,0,0,0,2,-1,0,0,1,3,1,1,0,1,0,0,1,1,1,0] |
| Phi over symmetry | [-2,0,0,0,1,1,0,1,1,1,3,0,1,0,1,0,1,0,1,0,-1] |
| Phi of -K | [-2,0,0,0,1,1,1,1,2,0,2,0,0,1,0,1,1,0,0,1,-1] |
| Phi of K* | [-1,-1,0,0,0,2,-1,0,0,1,2,1,1,0,0,0,-1,1,0,1,2] |
| Phi of -K* | [-2,0,0,0,1,1,0,1,1,1,3,0,1,0,1,0,1,0,1,0,-1] |
| Symmetry type of based matrix | c |
| u-polynomial | t^2-2t |
| Normalized Jones-Krushkal polynomial | 4z^2+23z+31 |
| Enhanced Jones-Krushkal polynomial | 4w^3z^2+23w^2z+31w |
| Inner characteristic polynomial | t^6+17t^4+18t^2+4 |
| Outer characteristic polynomial | t^7+23t^5+35t^3+9t |
| Flat arrow polynomial | -10*K1**2 + 5*K2 + 6 |
| 2-strand cable arrow polynomial | -192*K1**4*K2**2 + 768*K1**4*K2 - 1792*K1**4 + 224*K1**3*K2*K3 - 256*K1**3*K3 + 128*K1**2*K2**3 - 5552*K1**2*K2**2 - 96*K1**2*K2*K4 + 7440*K1**2*K2 - 96*K1**2*K3**2 - 4228*K1**2 - 64*K1*K2**2*K3 + 4560*K1*K2*K3 + 72*K1*K3*K4 - 104*K2**4 + 104*K2**2*K4 - 2944*K2**2 - 916*K3**2 - 30*K4**2 + 2972 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{4, 6}, {1, 5}, {2, 3}]] |
| If K is slice | False |