| Min(phi) over symmetries of the knot is: [-2,0,0,0,1,1,0,0,1,2,2,0,0,0,1,1,0,1,0,1,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.1836'] |
| 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+21t^5+29t^3+8t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1836'] |
| 2-strand cable arrow polynomial of the knot is: -192*K1**4*K2**2 + 832*K1**4*K2 - 2256*K1**4 + 224*K1**3*K2*K3 - 352*K1**3*K3 + 736*K1**2*K2**3 - 5552*K1**2*K2**2 - 832*K1**2*K2*K4 + 8408*K1**2*K2 - 112*K1**2*K3**2 - 5952*K1**2 + 160*K1*K2**3*K3 - 1184*K1*K2**2*K3 - 160*K1*K2**2*K5 - 32*K1*K2*K3*K4 + 7744*K1*K2*K3 + 1016*K1*K3*K4 + 48*K1*K4*K5 - 1192*K2**4 - 464*K2**2*K3**2 - 48*K2**2*K4**2 + 1928*K2**2*K4 - 4900*K2**2 + 392*K2*K3*K5 + 32*K2*K4*K6 - 2396*K3**2 - 738*K4**2 - 76*K5**2 - 4*K6**2 + 4920 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1836'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.73330', 'vk6.73340', 'vk6.73492', 'vk6.73501', 'vk6.75253', 'vk6.75266', 'vk6.75502', 'vk6.75510', 'vk6.78214', 'vk6.78230', 'vk6.78453', 'vk6.78472', 'vk6.80041', 'vk6.80056', 'vk6.80190', 'vk6.80204', 'vk6.81936', 'vk6.81937', 'vk6.82194', 'vk6.82212', 'vk6.82661', 'vk6.82665', 'vk6.84723', 'vk6.84729', 'vk6.85027', 'vk6.85029', 'vk6.85752', 'vk6.86506', 'vk6.87327', 'vk6.87690', 'vk6.89625', 'vk6.90088'] |
| 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 | O1O2O3U1U4O5U2O6O4U3U5U6 |
| R3 orbit | {'O1O2O3U1U4O5U2O6O4U3U5U6'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U4U5U1O6O4U2O5U6U3 |
| Gauss code of K* | O1O2O3U4U5U1O4O6U2O5U3U6 |
| Gauss code of -K* | O1O2O3U4U1O5U2O4O6U3U5U6 |
| 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 0 0 1 0 1],[ 2 0 1 2 1 2 1],[ 0 -1 0 0 0 1 1],[ 0 -2 0 0 0 0 1],[-1 -1 0 0 0 0 0],[ 0 -2 -1 0 0 0 1],[-1 -1 -1 -1 0 -1 0]] |
| Primitive based matrix | [[ 0 1 1 0 0 0 -2],[-1 0 0 0 0 0 -1],[-1 0 0 -1 -1 -1 -1],[ 0 0 1 0 1 0 -1],[ 0 0 1 -1 0 0 -2],[ 0 0 1 0 0 0 -2],[ 2 1 1 1 2 2 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-1,-1,0,0,0,2,0,0,0,0,1,1,1,1,1,-1,0,1,0,2,2] |
| Phi over symmetry | [-2,0,0,0,1,1,0,0,1,2,2,0,0,0,1,1,0,1,0,1,0] |
| Phi of -K | [-2,0,0,0,1,1,0,0,1,2,2,0,0,0,1,1,0,1,0,1,0] |
| Phi of K* | [-1,-1,0,0,0,2,0,0,0,0,2,1,1,1,2,-1,0,0,0,1,0] |
| Phi of -K* | [-2,0,0,0,1,1,1,2,2,1,1,0,1,0,1,0,0,1,0,1,0] |
| 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+15t^4+10t^2+1 |
| Outer characteristic polynomial | t^7+21t^5+29t^3+8t |
| Flat arrow polynomial | -6*K1**2 - 4*K1*K2 + 2*K1 + 3*K2 + 2*K3 + 4 |
| 2-strand cable arrow polynomial | -192*K1**4*K2**2 + 832*K1**4*K2 - 2256*K1**4 + 224*K1**3*K2*K3 - 352*K1**3*K3 + 736*K1**2*K2**3 - 5552*K1**2*K2**2 - 832*K1**2*K2*K4 + 8408*K1**2*K2 - 112*K1**2*K3**2 - 5952*K1**2 + 160*K1*K2**3*K3 - 1184*K1*K2**2*K3 - 160*K1*K2**2*K5 - 32*K1*K2*K3*K4 + 7744*K1*K2*K3 + 1016*K1*K3*K4 + 48*K1*K4*K5 - 1192*K2**4 - 464*K2**2*K3**2 - 48*K2**2*K4**2 + 1928*K2**2*K4 - 4900*K2**2 + 392*K2*K3*K5 + 32*K2*K4*K6 - 2396*K3**2 - 738*K4**2 - 76*K5**2 - 4*K6**2 + 4920 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {4, 5}, {2, 3}], [{2, 6}, {4, 5}, {1, 3}], [{4, 6}, {1, 5}, {2, 3}], [{5, 6}, {1, 4}, {2, 3}]] |
| If K is slice | False |