| Min(phi) over symmetries of the knot is: [-2,-1,0,1,1,1,0,1,1,1,2,0,0,1,1,1,1,1,1,0,-1] |
| Flat knots (up to 7 crossings) with same phi are :['6.962'] |
| 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+22t^5+32t^3 |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.962'] |
| 2-strand cable arrow polynomial of the knot is: -320*K1**6 - 192*K1**4*K2**2 + 576*K1**4*K2 - 1440*K1**4 + 128*K1**3*K2*K3 - 1088*K1**2*K2**2 + 2008*K1**2*K2 - 352*K1**2*K3**2 - 112*K1**2*K4**2 - 684*K1**2 + 1520*K1*K2*K3 + 520*K1*K3*K4 + 88*K1*K4*K5 - 184*K2**4 - 160*K2**2*K3**2 - 48*K2**2*K4**2 + 232*K2**2*K4 - 916*K2**2 + 120*K2*K3*K5 + 32*K2*K4*K6 - 576*K3**2 - 226*K4**2 - 36*K5**2 - 4*K6**2 + 1112 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.962'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.4078', 'vk6.4109', 'vk6.4249', 'vk6.4328', 'vk6.5316', 'vk6.5347', 'vk6.5526', 'vk6.5532', 'vk6.5645', 'vk6.5651', 'vk6.7469', 'vk6.7712', 'vk6.8939', 'vk6.8970', 'vk6.9114', 'vk6.9193', 'vk6.14547', 'vk6.15288', 'vk6.15417', 'vk6.15765', 'vk6.16182', 'vk6.26281', 'vk6.26724', 'vk6.29842', 'vk6.29873', 'vk6.33934', 'vk6.34214', 'vk6.38218', 'vk6.38233', 'vk6.44991', 'vk6.45010', 'vk6.48559', 'vk6.49177', 'vk6.49268', 'vk6.49290', 'vk6.50251', 'vk6.51592', 'vk6.53969', 'vk6.54470', 'vk6.63305'] |
| 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 | O1O2O3O4U5U2O6O5U6U4U1U3 |
| R3 orbit | {'O1O2O3O4U5U2O6O5U6U4U1U3', 'O1O2O3U4U1O5O4U5U6U2O6U3'} |
| R3 orbit length | 2 |
| Gauss code of -K | O1O2O3O4U2U4U1U5O6O5U3U6 |
| Gauss code of K* | O1O2O3O4U3U5U4U2O6O5U1U6 |
| Gauss code of -K* | O1O2O3O4U5U4O6O5U3U1U6U2 |
| 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 2 1 0 -1],[ 1 0 0 2 1 1 -1],[ 1 0 0 1 0 1 -1],[-2 -2 -1 0 0 -1 -1],[-1 -1 0 0 0 0 -1],[ 0 -1 -1 1 0 0 -1],[ 1 1 1 1 1 1 0]] |
| Primitive based matrix | [[ 0 2 1 0 -1 -1 -1],[-2 0 0 -1 -1 -1 -2],[-1 0 0 0 0 -1 -1],[ 0 1 0 0 -1 -1 -1],[ 1 1 0 1 0 -1 0],[ 1 1 1 1 1 0 1],[ 1 2 1 1 0 -1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,0,1,1,1,0,1,1,1,2,0,0,1,1,1,1,1,1,0,-1] |
| Phi over symmetry | [-2,-1,0,1,1,1,0,1,1,1,2,0,0,1,1,1,1,1,1,0,-1] |
| Phi of -K | [-1,-1,-1,0,1,2,-1,-1,0,1,2,0,0,1,1,0,2,2,1,1,1] |
| Phi of K* | [-2,-1,0,1,1,1,1,1,1,2,2,1,1,1,2,0,0,0,-1,0,1] |
| Phi of -K* | [-1,-1,-1,0,1,2,-1,0,1,0,1,1,1,1,1,1,1,2,0,1,0] |
| Symmetry type of based matrix | c |
| u-polynomial | -t^2+2t |
| Normalized Jones-Krushkal polynomial | 11z+23 |
| Enhanced Jones-Krushkal polynomial | 11w^2z+23w |
| Inner characteristic polynomial | t^6+14t^4+11t^2 |
| Outer characteristic polynomial | t^7+22t^5+32t^3 |
| Flat arrow polynomial | -6*K1**2 - 4*K1*K2 + 2*K1 + 3*K2 + 2*K3 + 4 |
| 2-strand cable arrow polynomial | -320*K1**6 - 192*K1**4*K2**2 + 576*K1**4*K2 - 1440*K1**4 + 128*K1**3*K2*K3 - 1088*K1**2*K2**2 + 2008*K1**2*K2 - 352*K1**2*K3**2 - 112*K1**2*K4**2 - 684*K1**2 + 1520*K1*K2*K3 + 520*K1*K3*K4 + 88*K1*K4*K5 - 184*K2**4 - 160*K2**2*K3**2 - 48*K2**2*K4**2 + 232*K2**2*K4 - 916*K2**2 + 120*K2*K3*K5 + 32*K2*K4*K6 - 576*K3**2 - 226*K4**2 - 36*K5**2 - 4*K6**2 + 1112 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {4, 5}, {2, 3}]] |
| If K is slice | False |