| Min(phi) over symmetries of the knot is: [-3,-1,0,1,1,2,0,2,1,3,3,1,1,1,1,1,1,2,-1,-1,1] |
| Flat knots (up to 7 crossings) with same phi are :['6.1295'] |
| Arrow polynomial of the knot is: -6*K1**2 - 2*K1*K2 + K1 + 3*K2 + K3 + 4 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.323', '6.380', '6.444', '6.472', '6.523', '6.579', '6.592', '6.595', '6.609', '6.614', '6.620', '6.644', '6.648', '6.669', '6.671', '6.681', '6.693', '6.724', '6.725', '6.757', '6.766', '6.785', '6.786', '6.797', '6.798', '6.816', '6.833', '6.972', '6.978', '6.1056', '6.1064', '6.1066', '6.1087', '6.1094', '6.1273', '6.1277', '6.1282', '6.1295', '6.1300', '6.1313', '6.1344', '6.1353', '6.1354'] |
| Outer characteristic polynomial of the knot is: t^7+46t^5+32t^3+5t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1295'] |
| 2-strand cable arrow polynomial of the knot is: -192*K1**6 - 128*K1**4*K2**2 + 1760*K1**4*K2 - 5568*K1**4 + 1152*K1**3*K2*K3 + 32*K1**3*K3*K4 - 1472*K1**3*K3 + 512*K1**2*K2**3 - 5120*K1**2*K2**2 - 1216*K1**2*K2*K4 + 9816*K1**2*K2 - 1184*K1**2*K3**2 - 496*K1**2*K4**2 - 4336*K1**2 - 672*K1*K2**2*K3 - 32*K1*K2*K3*K4 + 6752*K1*K2*K3 + 2088*K1*K3*K4 + 400*K1*K4*K5 - 408*K2**4 - 16*K2**2*K3**2 - 8*K2**2*K4**2 + 928*K2**2*K4 - 4086*K2**2 + 40*K2*K3*K5 + 8*K2*K4*K6 - 2032*K3**2 - 794*K4**2 - 88*K5**2 - 2*K6**2 + 4360 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1295'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.11481', 'vk6.11784', 'vk6.12803', 'vk6.13138', 'vk6.17032', 'vk6.17274', 'vk6.20861', 'vk6.20939', 'vk6.22270', 'vk6.22350', 'vk6.23759', 'vk6.28329', 'vk6.31246', 'vk6.31595', 'vk6.32819', 'vk6.35542', 'vk6.35991', 'vk6.39961', 'vk6.40106', 'vk6.42036', 'vk6.42953', 'vk6.43248', 'vk6.46500', 'vk6.46624', 'vk6.52234', 'vk6.53071', 'vk6.53387', 'vk6.55452', 'vk6.58864', 'vk6.59936', 'vk6.64409', 'vk6.69734'] |
| 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 | O1O2O3U2O4O5U6U1O6U4U3U5 |
| R3 orbit | {'O1O2O3U2O4O5U6U1O6U4U3U5'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U4U1U5O6U3U6O4O5U2 |
| Gauss code of K* | O1O2O3U4U5U2O5U1U3O6O4U6 |
| Gauss code of -K* | O1O2O3U4O5O4U1U3O6U2U6U5 |
| 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 1 0 3 -1],[ 2 0 0 2 0 2 2],[ 1 0 0 1 0 1 1],[-1 -2 -1 0 0 2 -1],[ 0 0 0 0 0 1 0],[-3 -2 -1 -2 -1 0 -3],[ 1 -2 -1 1 0 3 0]] |
| Primitive based matrix | [[ 0 3 1 0 -1 -1 -2],[-3 0 -2 -1 -1 -3 -2],[-1 2 0 0 -1 -1 -2],[ 0 1 0 0 0 0 0],[ 1 1 1 0 0 1 0],[ 1 3 1 0 -1 0 -2],[ 2 2 2 0 0 2 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-3,-1,0,1,1,2,2,1,1,3,2,0,1,1,2,0,0,0,-1,0,2] |
| Phi over symmetry | [-3,-1,0,1,1,2,0,2,1,3,3,1,1,1,1,1,1,2,-1,-1,1] |
| Phi of -K | [-2,-1,-1,0,1,3,-1,1,2,1,3,1,1,1,1,1,1,3,1,2,0] |
| Phi of K* | [-3,-1,0,1,1,2,0,2,1,3,3,1,1,1,1,1,1,2,-1,-1,1] |
| Phi of -K* | [-2,-1,-1,0,1,3,0,2,0,2,2,1,0,1,1,0,1,3,0,1,2] |
| Symmetry type of based matrix | c |
| u-polynomial | -t^3+t^2+t |
| Normalized Jones-Krushkal polynomial | 4z^2+25z+35 |
| Enhanced Jones-Krushkal polynomial | 4w^3z^2+25w^2z+35w |
| Inner characteristic polynomial | t^6+30t^4+11t^2 |
| Outer characteristic polynomial | t^7+46t^5+32t^3+5t |
| Flat arrow polynomial | -6*K1**2 - 2*K1*K2 + K1 + 3*K2 + K3 + 4 |
| 2-strand cable arrow polynomial | -192*K1**6 - 128*K1**4*K2**2 + 1760*K1**4*K2 - 5568*K1**4 + 1152*K1**3*K2*K3 + 32*K1**3*K3*K4 - 1472*K1**3*K3 + 512*K1**2*K2**3 - 5120*K1**2*K2**2 - 1216*K1**2*K2*K4 + 9816*K1**2*K2 - 1184*K1**2*K3**2 - 496*K1**2*K4**2 - 4336*K1**2 - 672*K1*K2**2*K3 - 32*K1*K2*K3*K4 + 6752*K1*K2*K3 + 2088*K1*K3*K4 + 400*K1*K4*K5 - 408*K2**4 - 16*K2**2*K3**2 - 8*K2**2*K4**2 + 928*K2**2*K4 - 4086*K2**2 + 40*K2*K3*K5 + 8*K2*K4*K6 - 2032*K3**2 - 794*K4**2 - 88*K5**2 - 2*K6**2 + 4360 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{5, 6}, {2, 4}, {1, 3}]] |
| If K is slice | False |