| Min(phi) over symmetries of the knot is: [-2,-2,0,1,1,2,-1,1,1,2,2,1,1,2,1,1,0,1,-1,0,2] |
| Flat knots (up to 7 crossings) with same phi are :['6.542'] |
| Arrow polynomial of the knot is: 4*K1**3 - 10*K1**2 - 4*K1*K2 - K1 + 5*K2 + K3 + 6 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.241', '6.341', '6.542', '6.567', '6.699', '6.713', '6.771', '6.791', '6.1025', '6.1039', '6.1041', '6.1072', '6.1077', '6.1121', '6.1123', '6.1499', '6.1502', '6.1531', '6.1645', '6.1648', '6.1726', '6.1727', '6.1761', '6.1784', '6.1807', '6.1823', '6.1832', '6.1869', '6.1873', '6.1874'] |
| Outer characteristic polynomial of the knot is: t^7+45t^5+30t^3+4t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.542'] |
| 2-strand cable arrow polynomial of the knot is: -1792*K1**4*K2**2 + 3424*K1**4*K2 - 4928*K1**4 + 1056*K1**3*K2*K3 - 832*K1**3*K3 - 960*K1**2*K2**4 + 4128*K1**2*K2**3 + 128*K1**2*K2**2*K4 - 11248*K1**2*K2**2 - 864*K1**2*K2*K4 + 10624*K1**2*K2 - 256*K1**2*K3**2 - 3640*K1**2 + 1088*K1*K2**3*K3 - 1792*K1*K2**2*K3 - 160*K1*K2**2*K5 - 64*K1*K2*K3*K4 + 7048*K1*K2*K3 + 272*K1*K3*K4 + 8*K1*K4*K5 - 32*K2**6 + 64*K2**4*K4 - 2232*K2**4 - 400*K2**2*K3**2 - 48*K2**2*K4**2 + 1456*K2**2*K4 - 2478*K2**2 + 136*K2*K3*K5 + 16*K2*K4*K6 - 968*K3**2 - 114*K4**2 - 8*K5**2 - 2*K6**2 + 3368 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.542'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.13373', 'vk6.13444', 'vk6.13633', 'vk6.13753', 'vk6.14160', 'vk6.14397', 'vk6.15628', 'vk6.16086', 'vk6.16460', 'vk6.16475', 'vk6.17644', 'vk6.22859', 'vk6.22890', 'vk6.24193', 'vk6.33124', 'vk6.33161', 'vk6.33223', 'vk6.33282', 'vk6.34840', 'vk6.34871', 'vk6.36448', 'vk6.42434', 'vk6.42449', 'vk6.43546', 'vk6.53549', 'vk6.53584', 'vk6.53615', 'vk6.53681', 'vk6.54716', 'vk6.55682', 'vk6.60232', 'vk6.64579'] |
| 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 | O1O2O3O4O5U3U4U1O6U5U6U2 |
| R3 orbit | {'O1O2O3O4O5U3U4U1O6U5U6U2'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4O5U4U6U1O6U5U2U3 |
| Gauss code of K* | O1O2O3U4O5O4O6U3U6U1U2U5 |
| Gauss code of -K* | O1O2O3U2O4O5O6U3U5U6U1U4 |
| 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 -2 0 2 1],[ 2 0 2 -1 1 3 1],[-1 -2 0 -2 0 1 1],[ 2 1 2 0 1 2 1],[ 0 -1 0 -1 0 1 1],[-2 -3 -1 -2 -1 0 1],[-1 -1 -1 -1 -1 -1 0]] |
| Primitive based matrix | [[ 0 2 1 1 0 -2 -2],[-2 0 1 -1 -1 -2 -3],[-1 -1 0 -1 -1 -1 -1],[-1 1 1 0 0 -2 -2],[ 0 1 1 0 0 -1 -1],[ 2 2 1 2 1 0 1],[ 2 3 1 2 1 -1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,-1,0,2,2,-1,1,1,2,3,1,1,1,1,0,2,2,1,1,-1] |
| Phi over symmetry | [-2,-2,0,1,1,2,-1,1,1,2,2,1,1,2,1,1,0,1,-1,0,2] |
| Phi of -K | [-2,-2,0,1,1,2,-1,1,1,2,2,1,1,2,1,1,0,1,-1,0,2] |
| Phi of K* | [-2,-1,-1,0,2,2,0,2,1,1,2,1,1,1,1,0,2,2,1,1,-1] |
| Phi of -K* | [-2,-2,0,1,1,2,-1,1,1,2,3,1,1,2,2,1,0,1,-1,-1,1] |
| Symmetry type of based matrix | c |
| u-polynomial | t^2-2t |
| Normalized Jones-Krushkal polynomial | 5z^2+26z+33 |
| Enhanced Jones-Krushkal polynomial | 5w^3z^2+26w^2z+33w |
| Inner characteristic polynomial | t^6+31t^4+13t^2+1 |
| Outer characteristic polynomial | t^7+45t^5+30t^3+4t |
| Flat arrow polynomial | 4*K1**3 - 10*K1**2 - 4*K1*K2 - K1 + 5*K2 + K3 + 6 |
| 2-strand cable arrow polynomial | -1792*K1**4*K2**2 + 3424*K1**4*K2 - 4928*K1**4 + 1056*K1**3*K2*K3 - 832*K1**3*K3 - 960*K1**2*K2**4 + 4128*K1**2*K2**3 + 128*K1**2*K2**2*K4 - 11248*K1**2*K2**2 - 864*K1**2*K2*K4 + 10624*K1**2*K2 - 256*K1**2*K3**2 - 3640*K1**2 + 1088*K1*K2**3*K3 - 1792*K1*K2**2*K3 - 160*K1*K2**2*K5 - 64*K1*K2*K3*K4 + 7048*K1*K2*K3 + 272*K1*K3*K4 + 8*K1*K4*K5 - 32*K2**6 + 64*K2**4*K4 - 2232*K2**4 - 400*K2**2*K3**2 - 48*K2**2*K4**2 + 1456*K2**2*K4 - 2478*K2**2 + 136*K2*K3*K5 + 16*K2*K4*K6 - 968*K3**2 - 114*K4**2 - 8*K5**2 - 2*K6**2 + 3368 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{2, 6}, {1, 5}, {3, 4}], [{2, 6}, {1, 5}, {4}, {3}], [{3, 6}, {1, 5}, {2, 4}], [{3, 6}, {1, 5}, {4}, {2}], [{4, 6}, {1, 5}, {2, 3}], [{6}, {1, 5}, {4}, {2, 3}]] |
| If K is slice | False |