| Min(phi) over symmetries of the knot is: [-2,-1,0,1,1,1,0,1,0,1,3,1,0,0,1,1,0,-1,0,-1,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.1606'] |
| 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+24t^5+46t^3 |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1606'] |
| 2-strand cable arrow polynomial of the knot is: -512*K1**6 - 192*K1**4*K2**2 + 1184*K1**4*K2 - 3440*K1**4 + 192*K1**3*K2*K3 - 1984*K1**2*K2**2 + 4592*K1**2*K2 - 144*K1**2*K3**2 - 1000*K1**2 + 1616*K1*K2*K3 + 136*K1*K3*K4 - 72*K2**4 + 96*K2**2*K4 - 1640*K2**2 - 448*K3**2 - 74*K4**2 + 1688 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1606'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.4439', 'vk6.4536', 'vk6.5825', 'vk6.5954', 'vk6.7885', 'vk6.7999', 'vk6.9312', 'vk6.9433', 'vk6.13402', 'vk6.13499', 'vk6.13690', 'vk6.14059', 'vk6.15034', 'vk6.15156', 'vk6.17792', 'vk6.17825', 'vk6.18844', 'vk6.19428', 'vk6.19723', 'vk6.24339', 'vk6.25441', 'vk6.25474', 'vk6.26606', 'vk6.33248', 'vk6.33309', 'vk6.37571', 'vk6.44889', 'vk6.48644', 'vk6.50544', 'vk6.53656', 'vk6.55825', 'vk6.65489'] |
| 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 | O1O2O3U2O4U1U4O5U3O6U5U6 |
| R3 orbit | {'O1O2O3U2O4U1U4O5U3O6U5U6'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U4U5O4U1O5U6U3O6U2 |
| Gauss code of K* | O1O2U3O4U5O3O5U1U6U4O6U2 |
| Gauss code of -K* | O1O2U1O3U2O4O5U4O6U3U6U5 |
| 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 -2 -1 1 1 0 1],[ 2 0 0 3 1 1 0],[ 1 0 0 1 0 1 0],[-1 -3 -1 0 0 1 1],[-1 -1 0 0 0 0 0],[ 0 -1 -1 -1 0 0 1],[-1 0 0 -1 0 -1 0]] |
| Primitive based matrix | [[ 0 1 1 1 0 -1 -2],[-1 0 1 0 1 -1 -3],[-1 -1 0 0 -1 0 0],[-1 0 0 0 0 0 -1],[ 0 -1 1 0 0 -1 -1],[ 1 1 0 0 1 0 0],[ 2 3 0 1 1 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-1,-1,-1,0,1,2,-1,0,-1,1,3,0,1,0,0,0,0,1,1,1,0] |
| Phi over symmetry | [-2,-1,0,1,1,1,0,1,0,1,3,1,0,0,1,1,0,-1,0,-1,0] |
| Phi of -K | [-2,-1,0,1,1,1,1,1,0,2,3,0,1,2,2,2,1,0,0,-1,0] |
| Phi of K* | [-1,-1,-1,0,1,2,-1,0,0,2,3,0,2,1,0,1,2,2,0,1,1] |
| Phi of -K* | [-2,-1,0,1,1,1,0,1,0,1,3,1,0,0,1,1,0,-1,0,-1,0] |
| Symmetry type of based matrix | c |
| u-polynomial | t^2-2t |
| Normalized Jones-Krushkal polynomial | 15z+31 |
| Enhanced Jones-Krushkal polynomial | 15w^2z+31w |
| Inner characteristic polynomial | t^6+16t^4+13t^2 |
| Outer characteristic polynomial | t^7+24t^5+46t^3 |
| Flat arrow polynomial | -10*K1**2 + 5*K2 + 6 |
| 2-strand cable arrow polynomial | -512*K1**6 - 192*K1**4*K2**2 + 1184*K1**4*K2 - 3440*K1**4 + 192*K1**3*K2*K3 - 1984*K1**2*K2**2 + 4592*K1**2*K2 - 144*K1**2*K3**2 - 1000*K1**2 + 1616*K1*K2*K3 + 136*K1*K3*K4 - 72*K2**4 + 96*K2**2*K4 - 1640*K2**2 - 448*K3**2 - 74*K4**2 + 1688 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {4, 5}, {2, 3}], [{2, 6}, {1, 5}, {3, 4}], [{2, 6}, {3, 5}, {1, 4}], [{2, 6}, {4, 5}, {1, 3}], [{4, 6}, {1, 5}, {2, 3}], [{5, 6}, {1, 4}, {2, 3}]] |
| If K is slice | False |