| Min(phi) over symmetries of the knot is: [-2,0,0,0,1,1,1,1,1,1,1,-1,0,1,1,0,0,1,0,0,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.1962'] |
| 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+15t^5+24t^3+5t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1962'] |
| 2-strand cable arrow polynomial of the knot is: -64*K1**6 + 2016*K1**4*K2 - 6160*K1**4 + 32*K1**3*K2*K3 - 1696*K1**3*K3 + 768*K1**2*K2**3 - 6368*K1**2*K2**2 - 576*K1**2*K2*K4 + 12528*K1**2*K2 - 80*K1**2*K3**2 - 5676*K1**2 - 992*K1*K2**2*K3 + 7472*K1*K2*K3 + 784*K1*K3*K4 - 776*K2**4 + 1232*K2**2*K4 - 5040*K2**2 - 1988*K3**2 - 502*K4**2 + 5084 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1962'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.16933', 'vk6.17175', 'vk6.20547', 'vk6.21948', 'vk6.23330', 'vk6.23624', 'vk6.28001', 'vk6.29468', 'vk6.35376', 'vk6.35797', 'vk6.39413', 'vk6.41606', 'vk6.42849', 'vk6.43128', 'vk6.45989', 'vk6.47665', 'vk6.55096', 'vk6.55352', 'vk6.57427', 'vk6.58598', 'vk6.59495', 'vk6.59789', 'vk6.62094', 'vk6.63072', 'vk6.64947', 'vk6.65154', 'vk6.66967', 'vk6.67828', 'vk6.68237', 'vk6.68379', 'vk6.69578', 'vk6.70275'] |
| 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 | O1O2U1O3O4U5U2O6U3O5U6U4 |
| R3 orbit | {'O1O2U1O3O4U5U2O6U3O5U6U4'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2U3O4O3U1U5O6U2O5U4U6 |
| Gauss code of K* | O1O2U3O4U1O3O5U6U2O6U4U5 |
| Gauss code of -K* | O1O2U3O4U2O5O3U1U4O6U5U6 |
| 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 -1 0 0 2 -1 0],[ 1 0 1 1 1 0 0],[ 0 -1 0 1 1 -1 0],[ 0 -1 -1 0 1 0 0],[-2 -1 -1 -1 0 -1 -1],[ 1 0 1 0 1 0 0],[ 0 0 0 0 1 0 0]] |
| Primitive based matrix | [[ 0 2 0 0 0 -1 -1],[-2 0 -1 -1 -1 -1 -1],[ 0 1 0 1 0 -1 -1],[ 0 1 -1 0 0 0 -1],[ 0 1 0 0 0 0 0],[ 1 1 1 0 0 0 0],[ 1 1 1 1 0 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,0,0,0,1,1,1,1,1,1,1,-1,0,1,1,0,0,1,0,0,0] |
| Phi over symmetry | [-2,0,0,0,1,1,1,1,1,1,1,-1,0,1,1,0,0,1,0,0,0] |
| Phi of -K | [-1,-1,0,0,0,2,0,0,0,1,2,0,1,1,2,-1,0,1,0,1,1] |
| Phi of K* | [-2,0,0,0,1,1,1,1,1,2,2,-1,0,0,1,0,0,0,1,1,0] |
| Phi of -K* | [-1,-1,0,0,0,2,0,0,0,1,1,0,1,1,1,0,0,1,-1,1,1] |
| Symmetry type of based matrix | c |
| u-polynomial | -t^2+2t |
| Normalized Jones-Krushkal polynomial | 3z^2+24z+37 |
| Enhanced Jones-Krushkal polynomial | 3w^3z^2+24w^2z+37w |
| Inner characteristic polynomial | t^6+9t^4+11t^2+1 |
| Outer characteristic polynomial | t^7+15t^5+24t^3+5t |
| Flat arrow polynomial | -10*K1**2 + 5*K2 + 6 |
| 2-strand cable arrow polynomial | -64*K1**6 + 2016*K1**4*K2 - 6160*K1**4 + 32*K1**3*K2*K3 - 1696*K1**3*K3 + 768*K1**2*K2**3 - 6368*K1**2*K2**2 - 576*K1**2*K2*K4 + 12528*K1**2*K2 - 80*K1**2*K3**2 - 5676*K1**2 - 992*K1*K2**2*K3 + 7472*K1*K2*K3 + 784*K1*K3*K4 - 776*K2**4 + 1232*K2**2*K4 - 5040*K2**2 - 1988*K3**2 - 502*K4**2 + 5084 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{3, 6}, {1, 5}, {2, 4}], [{3, 6}, {2, 5}, {1, 4}], [{3, 6}, {4, 5}, {1, 2}], [{4, 6}, {2, 5}, {1, 3}], [{5, 6}, {3, 4}, {1, 2}], [{5, 6}, {3, 4}, {2}, {1}]] |
| If K is slice | False |