| Min(phi) over symmetries of the knot is: [-3,-1,0,0,2,2,1,1,2,2,3,0,0,1,1,0,1,1,1,1,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.1375'] |
| Arrow polynomial of the knot is: -8*K1**2 - 2*K1*K2 + K1 + 4*K2 + K3 + 5 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.377', '6.638', '6.646', '6.647', '6.657', '6.658', '6.662', '6.692', '6.695', '6.714', '6.720', '6.726', '6.730', '6.731', '6.749', '6.756', '6.772', '6.779', '6.781', '6.800', '6.829', '6.1085', '6.1089', '6.1302', '6.1349', '6.1350', '6.1360', '6.1362', '6.1375', '6.1384'] |
| Outer characteristic polynomial of the knot is: t^7+51t^5+37t^3+4t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1375'] |
| 2-strand cable arrow polynomial of the knot is: 64*K1**4*K2 - 2544*K1**4 + 320*K1**3*K2*K3 - 672*K1**3*K3 + 32*K1**2*K2**2*K4 - 2480*K1**2*K2**2 + 96*K1**2*K2*K3**2 - 512*K1**2*K2*K4 + 7064*K1**2*K2 - 976*K1**2*K3**2 - 96*K1**2*K3*K5 - 160*K1**2*K4**2 - 4884*K1**2 - 512*K1*K2**2*K3 - 32*K1*K2**2*K5 - 128*K1*K2*K3*K4 + 5696*K1*K2*K3 + 1600*K1*K3*K4 + 216*K1*K4*K5 - 128*K2**4 - 128*K2**2*K3**2 - 8*K2**2*K4**2 + 640*K2**2*K4 - 3942*K2**2 + 200*K2*K3*K5 + 8*K2*K4*K6 - 2076*K3**2 - 600*K4**2 - 88*K5**2 - 2*K6**2 + 4030 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1375'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.73288', 'vk6.73296', 'vk6.73429', 'vk6.73437', 'vk6.74085', 'vk6.74101', 'vk6.74654', 'vk6.74670', 'vk6.75433', 'vk6.75441', 'vk6.76119', 'vk6.76135', 'vk6.78161', 'vk6.78169', 'vk6.78391', 'vk6.78399', 'vk6.79095', 'vk6.79111', 'vk6.79986', 'vk6.79994', 'vk6.80137', 'vk6.80145', 'vk6.80599', 'vk6.80615', 'vk6.83811', 'vk6.83813', 'vk6.85130', 'vk6.85134', 'vk6.86616', 'vk6.86620', 'vk6.87376', 'vk6.87384'] |
| 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 | O1O2O3U4O5O6U1U3U6O4U2U5 |
| R3 orbit | {'O1O2O3U4O5O6U1U3U6O4U2U5'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U4U2O5U6U1U3O6O4U5 |
| Gauss code of K* | O1O2O3U4O5O6U1U5U2O4U6U3 |
| Gauss code of -K* | O1O2O3U1U4O5U2U6U3O4O6U5 |
| 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 -3 0 0 -1 2 2],[ 3 0 2 1 1 3 2],[ 0 -2 0 0 -1 1 1],[ 0 -1 0 0 -1 1 1],[ 1 -1 1 1 0 2 2],[-2 -3 -1 -1 -2 0 0],[-2 -2 -1 -1 -2 0 0]] |
| Primitive based matrix | [[ 0 2 2 0 0 -1 -3],[-2 0 0 -1 -1 -2 -2],[-2 0 0 -1 -1 -2 -3],[ 0 1 1 0 0 -1 -1],[ 0 1 1 0 0 -1 -2],[ 1 2 2 1 1 0 -1],[ 3 2 3 1 2 1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-2,0,0,1,3,0,1,1,2,2,1,1,2,3,0,1,1,1,2,1] |
| Phi over symmetry | [-3,-1,0,0,2,2,1,1,2,2,3,0,0,1,1,0,1,1,1,1,0] |
| Phi of -K | [-3,-1,0,0,2,2,1,1,2,2,3,0,0,1,1,0,1,1,1,1,0] |
| Phi of K* | [-2,-2,0,0,1,3,0,1,1,1,2,1,1,1,3,0,0,1,0,2,1] |
| Phi of -K* | [-3,-1,0,0,2,2,1,1,2,2,3,1,1,2,2,0,1,1,1,1,0] |
| Symmetry type of based matrix | c |
| u-polynomial | t^3-2t^2+t |
| Normalized Jones-Krushkal polynomial | 17z+35 |
| Enhanced Jones-Krushkal polynomial | 17w^2z+35w |
| Inner characteristic polynomial | t^6+33t^4+15t^2 |
| Outer characteristic polynomial | t^7+51t^5+37t^3+4t |
| Flat arrow polynomial | -8*K1**2 - 2*K1*K2 + K1 + 4*K2 + K3 + 5 |
| 2-strand cable arrow polynomial | 64*K1**4*K2 - 2544*K1**4 + 320*K1**3*K2*K3 - 672*K1**3*K3 + 32*K1**2*K2**2*K4 - 2480*K1**2*K2**2 + 96*K1**2*K2*K3**2 - 512*K1**2*K2*K4 + 7064*K1**2*K2 - 976*K1**2*K3**2 - 96*K1**2*K3*K5 - 160*K1**2*K4**2 - 4884*K1**2 - 512*K1*K2**2*K3 - 32*K1*K2**2*K5 - 128*K1*K2*K3*K4 + 5696*K1*K2*K3 + 1600*K1*K3*K4 + 216*K1*K4*K5 - 128*K2**4 - 128*K2**2*K3**2 - 8*K2**2*K4**2 + 640*K2**2*K4 - 3942*K2**2 + 200*K2*K3*K5 + 8*K2*K4*K6 - 2076*K3**2 - 600*K4**2 - 88*K5**2 - 2*K6**2 + 4030 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{2, 6}, {3, 5}, {1, 4}], [{2, 6}, {5}, {1, 4}, {3}]] |
| If K is slice | False |