| Min(phi) over symmetries of the knot is: [-2,0,0,0,1,1,0,1,1,2,2,0,1,0,0,1,0,0,0,1,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.1694'] |
| 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+43t^3+3t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1694'] |
| 2-strand cable arrow polynomial of the knot is: 192*K1**4*K2 - 2048*K1**4 - 288*K1**3*K3 - 1968*K1**2*K2**2 + 4752*K1**2*K2 - 32*K1**2*K3**2 - 2268*K1**2 - 192*K1*K2**2*K3 + 2368*K1*K2*K3 + 128*K1*K3*K4 - 360*K2**4 + 456*K2**2*K4 - 1936*K2**2 - 644*K3**2 - 146*K4**2 + 1984 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1694'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.16500', 'vk6.16591', 'vk6.18102', 'vk6.18440', 'vk6.22931', 'vk6.23026', 'vk6.24549', 'vk6.24968', 'vk6.34908', 'vk6.35015', 'vk6.36692', 'vk6.37116', 'vk6.42477', 'vk6.42588', 'vk6.43968', 'vk6.44285', 'vk6.54727', 'vk6.54822', 'vk6.55914', 'vk6.56204', 'vk6.59191', 'vk6.59254', 'vk6.60440', 'vk6.60799', 'vk6.64747', 'vk6.64804', 'vk6.65560', 'vk6.65872', 'vk6.68043', 'vk6.68106', 'vk6.68638', 'vk6.68853', 'vk6.73717', 'vk6.73834', 'vk6.78308', 'vk6.78488', 'vk6.78633', 'vk6.78826', 'vk6.85168', 'vk6.89438'] |
| 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 | O1O2O3U4O5U3U6U1O4O6U5U2 |
| R3 orbit | {'O1O2O3U4U2O5U6U1O4O6U3U5', 'O1O2O3U4O5U3U6U1O4O6U5U2'} |
| R3 orbit length | 2 |
| Gauss code of -K | O1O2O3U2U4O5O6U3U5U1O4U6 |
| Gauss code of K* | O1O2O3U4U2O5O6U3U6U1O4U5 |
| Gauss code of -K* | O1O2O3U4O5U3U6U1O6O4U2U5 |
| 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 0 1 0 -2 1 0],[ 0 0 0 0 -1 0 1],[-1 0 0 0 -2 0 0],[ 0 0 0 0 0 0 1],[ 2 1 2 0 0 2 1],[-1 0 0 0 -2 0 -1],[ 0 -1 0 -1 -1 1 0]] |
| Primitive based matrix | [[ 0 1 1 0 0 0 -2],[-1 0 0 0 0 0 -2],[-1 0 0 0 0 -1 -2],[ 0 0 0 0 0 1 0],[ 0 0 0 0 0 1 -1],[ 0 0 1 -1 -1 0 -1],[ 2 2 2 0 1 1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-1,-1,0,0,0,2,0,0,0,0,2,0,0,1,2,0,-1,0,-1,1,1] |
| Phi over symmetry | [-2,0,0,0,1,1,0,1,1,2,2,0,1,0,0,1,0,0,0,1,0] |
| Phi of -K | [-2,0,0,0,1,1,1,1,2,1,1,-1,0,1,1,1,0,1,1,1,0] |
| Phi of K* | [-1,-1,0,0,0,2,0,0,1,1,1,1,1,1,1,-1,-1,1,0,1,2] |
| Phi of -K* | [-2,0,0,0,1,1,0,1,1,2,2,0,1,0,0,1,0,0,0,1,0] |
| Symmetry type of based matrix | c |
| u-polynomial | t^2-2t |
| Normalized Jones-Krushkal polynomial | z^2+14z+25 |
| Enhanced Jones-Krushkal polynomial | w^3z^2+14w^2z+25w |
| Inner characteristic polynomial | t^6+13t^4+26t^2 |
| Outer characteristic polynomial | t^7+19t^5+43t^3+3t |
| Flat arrow polynomial | -10*K1**2 + 5*K2 + 6 |
| 2-strand cable arrow polynomial | 192*K1**4*K2 - 2048*K1**4 - 288*K1**3*K3 - 1968*K1**2*K2**2 + 4752*K1**2*K2 - 32*K1**2*K3**2 - 2268*K1**2 - 192*K1*K2**2*K3 + 2368*K1*K2*K3 + 128*K1*K3*K4 - 360*K2**4 + 456*K2**2*K4 - 1936*K2**2 - 644*K3**2 - 146*K4**2 + 1984 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{4, 6}, {3, 5}, {1, 2}], [{4, 6}, {3, 5}, {2}, {1}]] |
| If K is slice | False |