| Min(phi) over symmetries of the knot is: [-2,-1,0,1,1,1,-1,1,1,1,2,1,0,0,1,0,1,0,0,1,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.1850'] |
| 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+20t^5+42t^3+8t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1850'] |
| 2-strand cable arrow polynomial of the knot is: 160*K1**4*K2 - 2192*K1**4 + 480*K1**3*K2*K3 + 32*K1**3*K3*K4 - 352*K1**3*K3 + 128*K1**2*K2**3 - 5872*K1**2*K2**2 + 32*K1**2*K2*K3**2 - 992*K1**2*K2*K4 + 9544*K1**2*K2 - 528*K1**2*K3**2 - 80*K1**2*K4**2 - 6852*K1**2 + 352*K1*K2**3*K3 - 1024*K1*K2**2*K3 - 224*K1*K2**2*K5 - 128*K1*K2*K3*K4 + 8720*K1*K2*K3 + 1496*K1*K3*K4 + 128*K1*K4*K5 - 568*K2**4 - 256*K2**2*K3**2 - 48*K2**2*K4**2 + 1240*K2**2*K4 - 5292*K2**2 + 232*K2*K3*K5 + 32*K2*K4*K6 - 2744*K3**2 - 658*K4**2 - 60*K5**2 - 4*K6**2 + 5296 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1850'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.11009', 'vk6.11088', 'vk6.12177', 'vk6.12284', 'vk6.18206', 'vk6.18541', 'vk6.24668', 'vk6.25090', 'vk6.30580', 'vk6.30675', 'vk6.31852', 'vk6.31899', 'vk6.36800', 'vk6.37254', 'vk6.44043', 'vk6.44383', 'vk6.51808', 'vk6.51875', 'vk6.52674', 'vk6.52768', 'vk6.56000', 'vk6.56273', 'vk6.60539', 'vk6.60879', 'vk6.63494', 'vk6.63538', 'vk6.63974', 'vk6.64018', 'vk6.65665', 'vk6.65947', 'vk6.68713', 'vk6.68921'] |
| 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 | O1O2O3U2U4O5U3O6O4U1U5U6 |
| R3 orbit | {'O1O2O3U2U4O5U3O6O4U1U5U6'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U4U5U3O6O4U1O5U6U2 |
| Gauss code of K* | O1O2O3U1U4U5O4O6U2O5U3U6 |
| Gauss code of -K* | O1O2O3U4U1O5U2O4O6U5U6U3 |
| 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 1 0 1],[ 2 0 -1 2 1 1 1],[ 1 1 0 1 0 1 0],[-1 -2 -1 0 -1 0 0],[-1 -1 0 1 0 0 0],[ 0 -1 -1 0 0 0 1],[-1 -1 0 0 0 -1 0]] |
| Primitive based matrix | [[ 0 1 1 1 0 -1 -2],[-1 0 1 0 0 0 -1],[-1 -1 0 0 0 -1 -2],[-1 0 0 0 -1 0 -1],[ 0 0 0 1 0 -1 -1],[ 1 0 1 0 1 0 1],[ 2 1 2 1 1 -1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-1,-1,-1,0,1,2,-1,0,0,0,1,0,0,1,2,1,0,1,1,1,-1] |
| Phi over symmetry | [-2,-1,0,1,1,1,-1,1,1,1,2,1,0,0,1,0,1,0,0,1,0] |
| Phi of -K | [-2,-1,0,1,1,1,2,1,1,2,2,0,1,2,2,1,0,1,0,1,0] |
| Phi of K* | [-1,-1,-1,0,1,2,-1,0,1,1,1,0,1,2,2,0,2,2,0,1,2] |
| Phi of -K* | [-2,-1,0,1,1,1,-1,1,1,1,2,1,0,0,1,0,1,0,0,1,0] |
| 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+12t^4+17t^2+1 |
| Outer characteristic polynomial | t^7+20t^5+42t^3+8t |
| Flat arrow polynomial | -6*K1**2 - 4*K1*K2 + 2*K1 + 3*K2 + 2*K3 + 4 |
| 2-strand cable arrow polynomial | 160*K1**4*K2 - 2192*K1**4 + 480*K1**3*K2*K3 + 32*K1**3*K3*K4 - 352*K1**3*K3 + 128*K1**2*K2**3 - 5872*K1**2*K2**2 + 32*K1**2*K2*K3**2 - 992*K1**2*K2*K4 + 9544*K1**2*K2 - 528*K1**2*K3**2 - 80*K1**2*K4**2 - 6852*K1**2 + 352*K1*K2**3*K3 - 1024*K1*K2**2*K3 - 224*K1*K2**2*K5 - 128*K1*K2*K3*K4 + 8720*K1*K2*K3 + 1496*K1*K3*K4 + 128*K1*K4*K5 - 568*K2**4 - 256*K2**2*K3**2 - 48*K2**2*K4**2 + 1240*K2**2*K4 - 5292*K2**2 + 232*K2*K3*K5 + 32*K2*K4*K6 - 2744*K3**2 - 658*K4**2 - 60*K5**2 - 4*K6**2 + 5296 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {2, 5}, {3, 4}]] |
| If K is slice | False |