| Min(phi) over symmetries of the knot is: [-2,-2,0,1,1,2,-1,0,1,2,3,0,1,2,2,0,0,1,-1,0,1] |
| Flat knots (up to 7 crossings) with same phi are :['6.1207'] |
| Arrow polynomial of the knot is: -6*K1**2 - 4*K1*K2 + 2*K1 + 3*K2 + 2*K3 + 4 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.239', '6.428', '6.470', '6.556', '6.700', '6.910', '6.962', '6.1006', '6.1013', '6.1038', '6.1207', '6.1224', '6.1225', '6.1269', '6.1270', '6.1308', '6.1319', '6.1320', '6.1323', '6.1485', '6.1551', '6.1579', '6.1581', '6.1660', '6.1672', '6.1679', '6.1711', '6.1719', '6.1732', '6.1745', '6.1748', '6.1827', '6.1836', '6.1838', '6.1850', '6.1866'] |
| Outer characteristic polynomial of the knot is: t^7+41t^5+37t^3+5t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1207'] |
| 2-strand cable arrow polynomial of the knot is: -64*K1**4*K2**2 + 288*K1**4*K2 - 2672*K1**4 + 96*K1**3*K2*K3 + 32*K1**3*K3*K4 - 128*K1**3*K3 - 2048*K1**2*K2**2 - 160*K1**2*K2*K4 + 5496*K1**2*K2 - 880*K1**2*K3**2 - 96*K1**2*K3*K5 - 96*K1**2*K4**2 - 32*K1**2*K5**2 - 3796*K1**2 - 192*K1*K2**2*K3 - 192*K1*K2*K3*K4 + 4064*K1*K2*K3 + 1744*K1*K3*K4 + 544*K1*K4*K5 + 80*K1*K5*K6 - 152*K2**4 - 80*K2**2*K3**2 - 16*K2**2*K4**2 + 728*K2**2*K4 - 3364*K2**2 + 360*K2*K3*K5 + 32*K2*K4*K6 - 1904*K3**2 - 1038*K4**2 - 364*K5**2 - 44*K6**2 + 3852 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1207'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.3567', 'vk6.3587', 'vk6.3593', 'vk6.3814', 'vk6.3816', 'vk6.3845', 'vk6.3847', 'vk6.6976', 'vk6.6990', 'vk6.7007', 'vk6.7021', 'vk6.7198', 'vk6.7208', 'vk6.7228', 'vk6.15342', 'vk6.15353', 'vk6.15469', 'vk6.15478', 'vk6.33975', 'vk6.34021', 'vk6.34042', 'vk6.34436', 'vk6.48211', 'vk6.48233', 'vk6.48373', 'vk6.49946', 'vk6.49965', 'vk6.49995', 'vk6.53987', 'vk6.54002', 'vk6.54043', 'vk6.54491'] |
| 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 | O1O2O3O4U2U4U5O6O5U1U6U3 |
| R3 orbit | {'O1O2O3O4U2U4U5O6O5U1U6U3'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U2U5U4O6O5U6U1U3 |
| Gauss code of K* | O1O2O3U4U3O5O4O6U5U1U6U2 |
| Gauss code of -K* | O1O2O3U4U2O4O5O6U5U1U6U3 |
| 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 -2 2 1 1 0],[ 2 0 -1 3 1 2 0],[ 2 1 0 2 1 2 0],[-2 -3 -2 0 0 -1 -1],[-1 -1 -1 0 0 -1 0],[-1 -2 -2 1 1 0 0],[ 0 0 0 1 0 0 0]] |
| Primitive based matrix | [[ 0 2 1 1 0 -2 -2],[-2 0 0 -1 -1 -2 -3],[-1 0 0 -1 0 -1 -1],[-1 1 1 0 0 -2 -2],[ 0 1 0 0 0 0 0],[ 2 2 1 2 0 0 1],[ 2 3 1 2 0 -1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,-1,0,2,2,0,1,1,2,3,1,0,1,1,0,2,2,0,0,-1] |
| Phi over symmetry | [-2,-2,0,1,1,2,-1,0,1,2,3,0,1,2,2,0,0,1,-1,0,1] |
| Phi of -K | [-2,-2,0,1,1,2,-1,2,1,2,2,2,1,2,1,1,1,1,-1,0,1] |
| Phi of K* | [-2,-1,-1,0,2,2,0,1,1,1,2,1,1,1,1,1,2,2,2,2,-1] |
| Phi of -K* | [-2,-2,0,1,1,2,-1,0,1,2,3,0,1,2,2,0,0,1,-1,0,1] |
| Symmetry type of based matrix | c |
| u-polynomial | t^2-2t |
| Normalized Jones-Krushkal polynomial | 17z+35 |
| Enhanced Jones-Krushkal polynomial | 17w^2z+35w |
| Inner characteristic polynomial | t^6+27t^4+20t^2+1 |
| Outer characteristic polynomial | t^7+41t^5+37t^3+5t |
| Flat arrow polynomial | -6*K1**2 - 4*K1*K2 + 2*K1 + 3*K2 + 2*K3 + 4 |
| 2-strand cable arrow polynomial | -64*K1**4*K2**2 + 288*K1**4*K2 - 2672*K1**4 + 96*K1**3*K2*K3 + 32*K1**3*K3*K4 - 128*K1**3*K3 - 2048*K1**2*K2**2 - 160*K1**2*K2*K4 + 5496*K1**2*K2 - 880*K1**2*K3**2 - 96*K1**2*K3*K5 - 96*K1**2*K4**2 - 32*K1**2*K5**2 - 3796*K1**2 - 192*K1*K2**2*K3 - 192*K1*K2*K3*K4 + 4064*K1*K2*K3 + 1744*K1*K3*K4 + 544*K1*K4*K5 + 80*K1*K5*K6 - 152*K2**4 - 80*K2**2*K3**2 - 16*K2**2*K4**2 + 728*K2**2*K4 - 3364*K2**2 + 360*K2*K3*K5 + 32*K2*K4*K6 - 1904*K3**2 - 1038*K4**2 - 364*K5**2 - 44*K6**2 + 3852 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {3, 5}, {2, 4}], [{3, 6}, {1, 5}, {2, 4}], [{3, 6}, {1, 5}, {4}, {2}]] |
| If K is slice | False |