| Min(phi) over symmetries of the knot is: [-2,-1,0,1,1,1,0,1,1,1,2,1,0,0,1,1,1,2,0,-1,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.1308'] |
| 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+30t^5+63t^3+11t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1308'] |
| 2-strand cable arrow polynomial of the knot is: -384*K1**6 + 1056*K1**4*K2 - 4288*K1**4 + 640*K1**3*K2*K3 + 64*K1**3*K3*K4 - 1504*K1**3*K3 - 3424*K1**2*K2**2 - 640*K1**2*K2*K4 + 9680*K1**2*K2 - 1408*K1**2*K3**2 - 240*K1**2*K4**2 - 6112*K1**2 - 352*K1*K2**2*K3 - 256*K1*K2*K3*K4 + 7784*K1*K2*K3 + 2096*K1*K3*K4 + 304*K1*K4*K5 - 120*K2**4 - 352*K2**2*K3**2 - 112*K2**2*K4**2 + 752*K2**2*K4 - 5180*K2**2 - 96*K2*K3**2*K4 + 400*K2*K3*K5 + 136*K2*K4*K6 + 24*K3**2*K6 - 2844*K3**2 - 854*K4**2 - 148*K5**2 - 28*K6**2 + 5404 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1308'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.4449', 'vk6.4546', 'vk6.5831', 'vk6.5960', 'vk6.7893', 'vk6.8009', 'vk6.9318', 'vk6.9439', 'vk6.13414', 'vk6.13511', 'vk6.13702', 'vk6.14071', 'vk6.15046', 'vk6.15168', 'vk6.17772', 'vk6.17805', 'vk6.18820', 'vk6.19438', 'vk6.19733', 'vk6.24319', 'vk6.25417', 'vk6.25450', 'vk6.26612', 'vk6.33268', 'vk6.33329', 'vk6.37547', 'vk6.44895', 'vk6.48638', 'vk6.50540', 'vk6.53660', 'vk6.55808', 'vk6.65478'] |
| 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 | O1O2O3U4O5O4U6U2O6U5U1U3 |
| R3 orbit | {'O1O2O3U4O5O4U6U2O6U5U1U3'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U1U3U4O5U2U5O6O4U6 |
| Gauss code of K* | O1O2O3U2U4U3O5U1U5O6O4U6 |
| Gauss code of -K* | O1O2O3U4O5O4U6U3O6U1U5U2 |
| 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 -1 -1 2 1 0 -1],[ 1 0 0 2 2 0 0],[ 1 0 0 1 1 -1 1],[-2 -2 -1 0 -1 -1 -2],[-1 -2 -1 1 0 0 -2],[ 0 0 1 1 0 0 0],[ 1 0 -1 2 2 0 0]] |
| Primitive based matrix | [[ 0 2 1 0 -1 -1 -1],[-2 0 -1 -1 -1 -2 -2],[-1 1 0 0 -1 -2 -2],[ 0 1 0 0 1 0 0],[ 1 1 1 -1 0 1 0],[ 1 2 2 0 -1 0 0],[ 1 2 2 0 0 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,0,1,1,1,1,1,1,2,2,0,1,2,2,-1,0,0,-1,0,0] |
| Phi over symmetry | [-2,-1,0,1,1,1,0,1,1,1,2,1,0,0,1,1,1,2,0,-1,0] |
| Phi of -K | [-1,-1,-1,0,1,2,-1,0,2,1,2,0,1,0,1,1,0,1,1,1,0] |
| Phi of K* | [-2,-1,0,1,1,1,0,1,1,1,2,1,0,0,1,1,1,2,0,-1,0] |
| Phi of -K* | [-1,-1,-1,0,1,2,-1,0,0,2,2,0,-1,1,1,0,2,2,0,1,1] |
| Symmetry type of based matrix | c |
| u-polynomial | -t^2+2t |
| Normalized Jones-Krushkal polynomial | 2z^2+23z+39 |
| Enhanced Jones-Krushkal polynomial | 2w^3z^2+23w^2z+39w |
| Inner characteristic polynomial | t^6+22t^4+42t^2+4 |
| Outer characteristic polynomial | t^7+30t^5+63t^3+11t |
| Flat arrow polynomial | -6*K1**2 - 4*K1*K2 + 2*K1 + 3*K2 + 2*K3 + 4 |
| 2-strand cable arrow polynomial | -384*K1**6 + 1056*K1**4*K2 - 4288*K1**4 + 640*K1**3*K2*K3 + 64*K1**3*K3*K4 - 1504*K1**3*K3 - 3424*K1**2*K2**2 - 640*K1**2*K2*K4 + 9680*K1**2*K2 - 1408*K1**2*K3**2 - 240*K1**2*K4**2 - 6112*K1**2 - 352*K1*K2**2*K3 - 256*K1*K2*K3*K4 + 7784*K1*K2*K3 + 2096*K1*K3*K4 + 304*K1*K4*K5 - 120*K2**4 - 352*K2**2*K3**2 - 112*K2**2*K4**2 + 752*K2**2*K4 - 5180*K2**2 - 96*K2*K3**2*K4 + 400*K2*K3*K5 + 136*K2*K4*K6 + 24*K3**2*K6 - 2844*K3**2 - 854*K4**2 - 148*K5**2 - 28*K6**2 + 5404 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{2, 6}, {3, 5}, {1, 4}], [{3, 6}, {2, 5}, {1, 4}], [{5, 6}, {1, 4}, {2, 3}]] |
| If K is slice | False |