| Min(phi) over symmetries of the knot is: [-2,-2,1,1,1,1,0,1,1,1,2,1,1,1,2,-1,0,0,1,0,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.1382'] |
| Arrow polynomial of the knot is: 4*K1**3 - 4*K1*K2 - K1 + K3 + 1 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.395', '6.430', '6.440', '6.548', '6.551', '6.774', '6.832', '6.887', '6.908', '6.911', '6.1205', '6.1332', '6.1339', '6.1341', '6.1346', '6.1382', '6.1488', '6.1651', '6.1655', '6.1686'] |
| Outer characteristic polynomial of the knot is: t^7+40t^5+28t^3 |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.547', '6.1382'] |
| 2-strand cable arrow polynomial of the knot is: -448*K1**2*K2**4 + 384*K1**2*K2**3 - 3280*K1**2*K2**2 + 2136*K1**2*K2 - 1208*K1**2 + 512*K1*K2**3*K3 + 2552*K1*K2*K3 + 88*K1*K3*K4 - 32*K2**6 + 64*K2**4*K4 - 608*K2**4 - 208*K2**2*K3**2 - 48*K2**2*K4**2 + 360*K2**2*K4 - 590*K2**2 + 32*K2*K3*K5 + 16*K2*K4*K6 - 560*K3**2 - 132*K4**2 - 2*K6**2 + 970 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1382'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.17000', 'vk6.17241', 'vk6.20529', 'vk6.21927', 'vk6.23409', 'vk6.23716', 'vk6.27982', 'vk6.29451', 'vk6.35472', 'vk6.35917', 'vk6.39384', 'vk6.41573', 'vk6.42908', 'vk6.43207', 'vk6.45957', 'vk6.47636', 'vk6.55169', 'vk6.55413', 'vk6.57400', 'vk6.58576', 'vk6.59551', 'vk6.59889', 'vk6.62067', 'vk6.63052', 'vk6.64973', 'vk6.65179', 'vk6.66942', 'vk6.67801', 'vk6.68265', 'vk6.68419', 'vk6.69553', 'vk6.70251'] |
| 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 | O1O2O3U4O5O6U3U2U6O4U1U5 |
| R3 orbit | {'O1O2O3U4O5O6U3U2U6O4U1U5'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U4U3O5U6U2U1O6O4U5 |
| Gauss code of K* | O1O2O3U4O5O6U5U2U1O4U6U3 |
| Gauss code of -K* | O1O2O3U1U4O5U3U2U6O4O6U5 |
| Diagrammatic symmetry type | c |
| Flat genus of the diagram | 2 |
| If K is checkerboard colorable | False |
| If K is almost classical | False |
| Based matrix from Gauss code | [[ 0 -1 -1 -1 -1 2 2],[ 1 0 0 0 -1 2 2],[ 1 0 0 0 -1 2 2],[ 1 0 0 0 0 1 1],[ 1 1 1 0 0 2 2],[-2 -2 -2 -1 -2 0 0],[-2 -2 -2 -1 -2 0 0]] |
| Primitive based matrix | [[ 0 2 2 -1 -1 -1 -1],[-2 0 0 -1 -2 -2 -2],[-2 0 0 -1 -2 -2 -2],[ 1 1 1 0 0 0 0],[ 1 2 2 0 0 1 1],[ 1 2 2 0 -1 0 0],[ 1 2 2 0 -1 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-2,1,1,1,1,0,1,2,2,2,1,2,2,2,0,0,0,-1,-1,0] |
| Phi over symmetry | [-2,-2,1,1,1,1,0,1,1,1,2,1,1,1,2,-1,0,0,1,0,0] |
| Phi of -K | [-1,-1,-1,-1,2,2,-1,-1,0,1,1,0,0,1,1,0,1,1,2,2,0] |
| Phi of K* | [-2,-2,1,1,1,1,0,1,1,1,2,1,1,1,2,-1,0,0,1,0,0] |
| Phi of -K* | [-1,-1,-1,-1,2,2,-1,0,0,2,2,0,1,2,2,0,1,1,2,2,0] |
| Symmetry type of based matrix | c |
| u-polynomial | -2t^2+4t |
| Normalized Jones-Krushkal polynomial | z+3 |
| Enhanced Jones-Krushkal polynomial | -16w^3z+17w^2z+3w |
| Inner characteristic polynomial | t^6+28t^4+4t^2 |
| Outer characteristic polynomial | t^7+40t^5+28t^3 |
| Flat arrow polynomial | 4*K1**3 - 4*K1*K2 - K1 + K3 + 1 |
| 2-strand cable arrow polynomial | -448*K1**2*K2**4 + 384*K1**2*K2**3 - 3280*K1**2*K2**2 + 2136*K1**2*K2 - 1208*K1**2 + 512*K1*K2**3*K3 + 2552*K1*K2*K3 + 88*K1*K3*K4 - 32*K2**6 + 64*K2**4*K4 - 608*K2**4 - 208*K2**2*K3**2 - 48*K2**2*K4**2 + 360*K2**2*K4 - 590*K2**2 + 32*K2*K3*K5 + 16*K2*K4*K6 - 560*K3**2 - 132*K4**2 - 2*K6**2 + 970 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {2, 5}, {3, 4}], [{2, 6}, {1, 5}, {3, 4}]] |
| If K is slice | False |