| Min(phi) over symmetries of the knot is: [-2,-1,0,1,1,1,0,1,1,2,2,1,0,1,1,1,1,1,0,0,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.1736', '7.37754'] |
| Arrow polynomial of the knot is: -10*K1**2 + 5*K2 + 6 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.947', '6.1027', '6.1399', '6.1430', '6.1433', '6.1442', '6.1465', '6.1469', '6.1476', '6.1505', '6.1529', '6.1606', '6.1612', '6.1613', '6.1616', '6.1649', '6.1694', '6.1736', '6.1768', '6.1771', '6.1774', '6.1884', '6.1886', '6.1887', '6.1889', '6.1960', '6.1962'] |
| Outer characteristic polynomial of the knot is: t^7+24t^5+18t^3+2t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1736', '7.37754'] |
| 2-strand cable arrow polynomial of the knot is: -448*K1**6 - 256*K1**4*K2**2 + 4384*K1**4*K2 - 8640*K1**4 + 224*K1**3*K2*K3 - 1184*K1**3*K3 + 1856*K1**2*K2**3 - 10736*K1**2*K2**2 - 544*K1**2*K2*K4 + 12144*K1**2*K2 - 64*K1**2*K3**2 - 1992*K1**2 - 896*K1*K2**2*K3 + 7024*K1*K2*K3 + 272*K1*K3*K4 - 1512*K2**4 + 1184*K2**2*K4 - 3040*K2**2 - 1144*K3**2 - 218*K4**2 + 3584 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1736'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.11482', 'vk6.11787', 'vk6.12800', 'vk6.13137', 'vk6.17048', 'vk6.17291', 'vk6.20854', 'vk6.20944', 'vk6.22262', 'vk6.22354', 'vk6.23772', 'vk6.28324', 'vk6.31247', 'vk6.31598', 'vk6.32818', 'vk6.35555', 'vk6.36006', 'vk6.39952', 'vk6.40112', 'vk6.42028', 'vk6.42962', 'vk6.43259', 'vk6.46496', 'vk6.46632', 'vk6.52235', 'vk6.53068', 'vk6.53386', 'vk6.55469', 'vk6.58850', 'vk6.59946', 'vk6.64408', 'vk6.69724'] |
| 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 | O1O2O3U2U4O5O6U1U6O4U3U5 |
| R3 orbit | {'O1O2O3U2U4O5O6U1U6O4U3U5'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U4U1O5U6U3O6O4U5U2 |
| Gauss code of K* | O1O2U3O4O5U1U6U4O6O3U5U2 |
| Gauss code of -K* | O1O2U3O4O5U4U1O3O6U2U6U5 |
| 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 1 1],[ 2 0 0 2 1 2 1],[ 1 0 0 1 1 1 0],[-1 -2 -1 0 -1 0 0],[ 0 -1 -1 1 0 1 1],[-1 -2 -1 0 -1 0 0],[-1 -1 0 0 -1 0 0]] |
| Primitive based matrix | [[ 0 1 1 1 0 -1 -2],[-1 0 0 0 -1 0 -1],[-1 0 0 0 -1 -1 -2],[-1 0 0 0 -1 -1 -2],[ 0 1 1 1 0 -1 -1],[ 1 0 1 1 1 0 0],[ 2 1 2 2 1 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-1,-1,-1,0,1,2,0,0,1,0,1,0,1,1,2,1,1,2,1,1,0] |
| Phi over symmetry | [-2,-1,0,1,1,1,0,1,1,2,2,1,0,1,1,1,1,1,0,0,0] |
| Phi of -K | [-2,-1,0,1,1,1,1,1,1,1,2,0,1,1,2,0,0,0,0,0,0] |
| Phi of K* | [-1,-1,-1,0,1,2,0,0,0,1,1,0,0,1,1,0,2,2,0,1,1] |
| Phi of -K* | [-2,-1,0,1,1,1,0,1,1,2,2,1,0,1,1,1,1,1,0,0,0] |
| Symmetry type of based matrix | c |
| u-polynomial | t^2-2t |
| Normalized Jones-Krushkal polynomial | 4z^2+25z+35 |
| Enhanced Jones-Krushkal polynomial | 4w^3z^2+25w^2z+35w |
| Inner characteristic polynomial | t^6+16t^4+9t^2 |
| Outer characteristic polynomial | t^7+24t^5+18t^3+2t |
| Flat arrow polynomial | -10*K1**2 + 5*K2 + 6 |
| 2-strand cable arrow polynomial | -448*K1**6 - 256*K1**4*K2**2 + 4384*K1**4*K2 - 8640*K1**4 + 224*K1**3*K2*K3 - 1184*K1**3*K3 + 1856*K1**2*K2**3 - 10736*K1**2*K2**2 - 544*K1**2*K2*K4 + 12144*K1**2*K2 - 64*K1**2*K3**2 - 1992*K1**2 - 896*K1*K2**2*K3 + 7024*K1*K2*K3 + 272*K1*K3*K4 - 1512*K2**4 + 1184*K2**2*K4 - 3040*K2**2 - 1144*K3**2 - 218*K4**2 + 3584 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {3, 5}, {2, 4}], [{1, 6}, {5}, {2, 4}, {3}], [{3, 6}, {4, 5}, {1, 2}], [{5, 6}, {3, 4}, {1, 2}]] |
| If K is slice | False |