| Min(phi) over symmetries of the knot is: [-2,0,0,0,1,1,0,1,1,0,2,-1,-1,1,0,-1,1,0,0,1,-1] |
| Flat knots (up to 7 crossings) with same phi are :['6.1399'] |
| 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+19t^5+49t^3+8t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1399'] |
| 2-strand cable arrow polynomial of the knot is: -64*K1**4*K2**2 + 1632*K1**4*K2 - 4960*K1**4 + 192*K1**3*K2*K3 - 1408*K1**3*K3 - 4144*K1**2*K2**2 - 64*K1**2*K2*K4 + 10576*K1**2*K2 - 288*K1**2*K3**2 - 5692*K1**2 - 320*K1*K2**2*K3 + 5904*K1*K2*K3 + 408*K1*K3*K4 - 104*K2**4 + 320*K2**2*K4 - 4704*K2**2 - 1772*K3**2 - 190*K4**2 + 4676 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1399'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.3556', 'vk6.3575', 'vk6.3605', 'vk6.3802', 'vk6.3828', 'vk6.3833', 'vk6.3859', 'vk6.6972', 'vk6.6994', 'vk6.7003', 'vk6.7025', 'vk6.7194', 'vk6.7212', 'vk6.7225', 'vk6.15341', 'vk6.15354', 'vk6.15466', 'vk6.15481', 'vk6.33978', 'vk6.34022', 'vk6.34041', 'vk6.34433', 'vk6.48215', 'vk6.48229', 'vk6.48376', 'vk6.49957', 'vk6.49977', 'vk6.49983', 'vk6.53990', 'vk6.53999', 'vk6.54044', 'vk6.54490'] |
| 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 | O1O2O3U1O4U3O5U4O6U5U6U2 |
| R3 orbit | {'O1O2O3U1O4U3O5U4O6U5U6U2'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U2U4U5O4U6O5U1O6U3 |
| Gauss code of K* | O1O2O3U4U3U5O4U6O5U1O6U2 |
| Gauss code of -K* | O1O2O3U2O4U3O5U4O6U5U1U6 |
| 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 1 0 0 0 1],[ 2 0 2 1 1 0 0],[-1 -2 0 -1 0 0 1],[ 0 -1 1 0 1 1 0],[ 0 -1 0 -1 0 1 1],[ 0 0 0 -1 -1 0 1],[-1 0 -1 0 -1 -1 0]] |
| Primitive based matrix | [[ 0 1 1 0 0 0 -2],[-1 0 1 0 0 -1 -2],[-1 -1 0 -1 -1 0 0],[ 0 0 1 0 1 -1 -1],[ 0 0 1 -1 0 -1 0],[ 0 1 0 1 1 0 -1],[ 2 2 0 1 0 1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-1,-1,0,0,0,2,-1,0,0,1,2,1,1,0,0,-1,1,1,1,0,1] |
| Phi over symmetry | [-2,0,0,0,1,1,0,1,1,0,2,-1,-1,1,0,-1,1,0,0,1,-1] |
| Phi of -K | [-2,0,0,0,1,1,1,1,2,1,3,-1,-1,0,1,-1,1,0,1,0,-1] |
| Phi of K* | [-1,-1,0,0,0,2,-1,0,0,1,3,1,1,0,1,-1,-1,2,-1,1,1] |
| Phi of -K* | [-2,0,0,0,1,1,0,1,1,0,2,-1,-1,1,0,-1,1,0,0,1,-1] |
| Symmetry type of based matrix | c |
| u-polynomial | t^2-2t |
| Normalized Jones-Krushkal polynomial | 21z+43 |
| Enhanced Jones-Krushkal polynomial | 21w^2z+43w |
| Inner characteristic polynomial | t^6+13t^4+20t^2+1 |
| Outer characteristic polynomial | t^7+19t^5+49t^3+8t |
| Flat arrow polynomial | -10*K1**2 + 5*K2 + 6 |
| 2-strand cable arrow polynomial | -64*K1**4*K2**2 + 1632*K1**4*K2 - 4960*K1**4 + 192*K1**3*K2*K3 - 1408*K1**3*K3 - 4144*K1**2*K2**2 - 64*K1**2*K2*K4 + 10576*K1**2*K2 - 288*K1**2*K3**2 - 5692*K1**2 - 320*K1*K2**2*K3 + 5904*K1*K2*K3 + 408*K1*K3*K4 - 104*K2**4 + 320*K2**2*K4 - 4704*K2**2 - 1772*K3**2 - 190*K4**2 + 4676 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{4, 6}, {2, 5}, {1, 3}], [{6}, {2, 5}, {4}, {1, 3}]] |
| If K is slice | False |