| Min(phi) over symmetries of the knot is: [-2,-1,0,1,1,1,0,1,1,1,1,0,1,1,2,0,1,1,0,0,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.1935'] |
| Arrow polynomial of the knot is: -2*K1**2 - 4*K1*K2 + 2*K1 + K2 + 2*K3 + 2 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.120', '6.213', '6.216', '6.320', '6.322', '6.615', '6.617', '6.891', '6.951', '6.955', '6.1001', '6.1012', '6.1022', '6.1043', '6.1047', '6.1063', '6.1074', '6.1249', '6.1544', '6.1546', '6.1555', '6.1573', '6.1574', '6.1585', '6.1756', '6.1757', '6.1762', '6.1802', '6.1803', '6.1824', '6.1881', '6.1935'] |
| Outer characteristic polynomial of the knot is: t^7+26t^5+47t^3+11t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1935'] |
| 2-strand cable arrow polynomial of the knot is: 736*K1**4*K2 - 2576*K1**4 + 384*K1**3*K2*K3 - 1248*K1**3*K3 + 32*K1**3*K4*K5 + 128*K1**2*K2**2*K4 - 2640*K1**2*K2**2 - 1216*K1**2*K2*K4 + 7656*K1**2*K2 - 464*K1**2*K3**2 - 176*K1**2*K4**2 - 96*K1**2*K5**2 - 6060*K1**2 - 704*K1*K2**2*K3 - 288*K1*K2**2*K5 - 416*K1*K2*K3*K4 + 6640*K1*K2*K3 - 64*K1*K2*K4*K5 + 2168*K1*K3*K4 + 656*K1*K4*K5 + 128*K1*K5*K6 - 104*K2**4 - 192*K2**2*K3**2 - 80*K2**2*K4**2 + 1696*K2**2*K4 - 5452*K2**2 + 1016*K2*K3*K5 + 152*K2*K4*K6 - 2808*K3**2 - 1462*K4**2 - 596*K5**2 - 84*K6**2 + 5332 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1935'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.4876', 'vk6.5219', 'vk6.6466', 'vk6.6885', 'vk6.8431', 'vk6.8850', 'vk6.9775', 'vk6.10066', 'vk6.11683', 'vk6.12034', 'vk6.13029', 'vk6.20494', 'vk6.20759', 'vk6.21855', 'vk6.27900', 'vk6.29402', 'vk6.29728', 'vk6.32680', 'vk6.33021', 'vk6.39331', 'vk6.39791', 'vk6.46355', 'vk6.47601', 'vk6.47932', 'vk6.48834', 'vk6.49103', 'vk6.51357', 'vk6.51568', 'vk6.53282', 'vk6.57355', 'vk6.64351', 'vk6.66908'] |
| 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 | O1O2O3U1U4U5O6O5O4U3U6U2 |
| R3 orbit | {'O1O2O3U1U4U5O6O5O4U3U6U2'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U2U1U4O5O6O4U6U3U5 |
| Gauss code of K* | O1O2O3U4U3U1O4O5O6U2U6U5 |
| Gauss code of -K* | O1O2O3U4U5U2O5O4O6U3U1U6 |
| 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 0 1 1 -1],[ 2 0 2 1 2 2 1],[-1 -2 0 -1 0 0 -1],[ 0 -1 1 0 0 0 -1],[-1 -2 0 0 0 0 0],[-1 -2 0 0 0 0 -1],[ 1 -1 1 1 0 1 0]] |
| Primitive based matrix | [[ 0 1 1 1 0 -1 -2],[-1 0 0 0 0 0 -2],[-1 0 0 0 0 -1 -2],[-1 0 0 0 -1 -1 -2],[ 0 0 0 1 0 -1 -1],[ 1 0 1 1 1 0 -1],[ 2 2 2 2 1 1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-1,-1,-1,0,1,2,0,0,0,0,2,0,0,1,2,1,1,2,1,1,1] |
| Phi over symmetry | [-2,-1,0,1,1,1,0,1,1,1,1,0,1,1,2,0,1,1,0,0,0] |
| Phi of -K | [-2,-1,0,1,1,1,0,1,1,1,1,0,1,1,2,0,1,1,0,0,0] |
| Phi of K* | [-1,-1,-1,0,1,2,0,0,0,1,1,0,1,1,1,1,2,1,0,1,0] |
| Phi of -K* | [-2,-1,0,1,1,1,1,1,2,2,2,1,0,1,1,0,0,1,0,0,0] |
| Symmetry type of based matrix | c |
| u-polynomial | t^2-2t |
| Normalized Jones-Krushkal polynomial | 6z^2+27z+31 |
| Enhanced Jones-Krushkal polynomial | 6w^3z^2+27w^2z+31w |
| Inner characteristic polynomial | t^6+18t^4+26t^2+4 |
| Outer characteristic polynomial | t^7+26t^5+47t^3+11t |
| Flat arrow polynomial | -2*K1**2 - 4*K1*K2 + 2*K1 + K2 + 2*K3 + 2 |
| 2-strand cable arrow polynomial | 736*K1**4*K2 - 2576*K1**4 + 384*K1**3*K2*K3 - 1248*K1**3*K3 + 32*K1**3*K4*K5 + 128*K1**2*K2**2*K4 - 2640*K1**2*K2**2 - 1216*K1**2*K2*K4 + 7656*K1**2*K2 - 464*K1**2*K3**2 - 176*K1**2*K4**2 - 96*K1**2*K5**2 - 6060*K1**2 - 704*K1*K2**2*K3 - 288*K1*K2**2*K5 - 416*K1*K2*K3*K4 + 6640*K1*K2*K3 - 64*K1*K2*K4*K5 + 2168*K1*K3*K4 + 656*K1*K4*K5 + 128*K1*K5*K6 - 104*K2**4 - 192*K2**2*K3**2 - 80*K2**2*K4**2 + 1696*K2**2*K4 - 5452*K2**2 + 1016*K2*K3*K5 + 152*K2*K4*K6 - 2808*K3**2 - 1462*K4**2 - 596*K5**2 - 84*K6**2 + 5332 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{4, 6}, {1, 5}, {2, 3}], [{4, 6}, {2, 5}, {1, 3}], [{4, 6}, {3, 5}, {1, 2}]] |
| If K is slice | False |