| Min(phi) over symmetries of the knot is: [-2,-2,0,1,1,2,-1,0,2,3,2,0,2,2,2,0,0,1,0,1,1] |
| Flat knots (up to 7 crossings) with same phi are :['6.470'] |
| 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+47t^5+58t^3+7t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.470'] |
| 2-strand cable arrow polynomial of the knot is: -512*K1**6 + 736*K1**4*K2 - 4256*K1**4 + 32*K1**3*K2*K3 + 32*K1**3*K3*K4 - 416*K1**3*K3 - 2176*K1**2*K2**2 - 384*K1**2*K2*K4 + 6896*K1**2*K2 - 2016*K1**2*K3**2 - 128*K1**2*K3*K5 - 560*K1**2*K4**2 - 32*K1**2*K4*K6 - 4516*K1**2 - 256*K1*K2**2*K3 - 160*K1*K2*K3*K4 + 6032*K1*K2*K3 + 3920*K1*K3*K4 + 952*K1*K4*K5 + 72*K1*K5*K6 - 88*K2**4 - 144*K2**2*K3**2 - 16*K2**2*K4**2 + 584*K2**2*K4 - 3884*K2**2 + 360*K2*K3*K5 + 72*K2*K4*K6 - 3044*K3**2 - 1694*K4**2 - 432*K5**2 - 60*K6**2 + 5084 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.470'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.4781', 'vk6.4783', 'vk6.5118', 'vk6.5120', 'vk6.6346', 'vk6.6776', 'vk6.6782', 'vk6.8300', 'vk6.8310', 'vk6.8752', 'vk6.9670', 'vk6.9684', 'vk6.9981', 'vk6.9995', 'vk6.21001', 'vk6.21030', 'vk6.22425', 'vk6.22452', 'vk6.28457', 'vk6.40229', 'vk6.40250', 'vk6.42160', 'vk6.46731', 'vk6.46752', 'vk6.48805', 'vk6.49022', 'vk6.49040', 'vk6.49838', 'vk6.49860', 'vk6.51497', 'vk6.58964', 'vk6.69806'] |
| 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 | O1O2O3O4O5U6U4O6U2U5U1U3 |
| R3 orbit | {'O1O2O3O4O5U6U4O6U2U5U1U3'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4O5U3U5U1U4O6U2U6 |
| Gauss code of K* | O1O2O3O4U3U1U4U5U2O6O5U6 |
| Gauss code of -K* | O1O2O3O4U5O6O5U3U6U1U4U2 |
| 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 -1 -2 2 0 2 -1],[ 1 0 -1 2 0 2 0],[ 2 1 0 2 1 2 1],[-2 -2 -2 0 0 1 -3],[ 0 0 -1 0 0 0 0],[-2 -2 -2 -1 0 0 -2],[ 1 0 -1 3 0 2 0]] |
| Primitive based matrix | [[ 0 2 2 0 -1 -1 -2],[-2 0 1 0 -2 -3 -2],[-2 -1 0 0 -2 -2 -2],[ 0 0 0 0 0 0 -1],[ 1 2 2 0 0 0 -1],[ 1 3 2 0 0 0 -1],[ 2 2 2 1 1 1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-2,0,1,1,2,-1,0,2,3,2,0,2,2,2,0,0,1,0,1,1] |
| Phi over symmetry | [-2,-2,0,1,1,2,-1,0,2,3,2,0,2,2,2,0,0,1,0,1,1] |
| Phi of -K | [-2,-1,-1,0,2,2,0,0,1,2,2,0,1,0,1,1,1,1,2,2,-1] |
| Phi of K* | [-2,-2,0,1,1,2,-1,2,1,1,2,2,0,1,2,1,1,1,0,0,0] |
| Phi of -K* | [-2,-1,-1,0,2,2,1,1,1,2,2,0,0,2,2,0,2,3,0,0,-1] |
| Symmetry type of based matrix | c |
| u-polynomial | -t^2+2t |
| Normalized Jones-Krushkal polynomial | 21z+43 |
| Enhanced Jones-Krushkal polynomial | 21w^2z+43w |
| Inner characteristic polynomial | t^6+33t^4+37t^2+4 |
| Outer characteristic polynomial | t^7+47t^5+58t^3+7t |
| Flat arrow polynomial | -6*K1**2 - 4*K1*K2 + 2*K1 + 3*K2 + 2*K3 + 4 |
| 2-strand cable arrow polynomial | -512*K1**6 + 736*K1**4*K2 - 4256*K1**4 + 32*K1**3*K2*K3 + 32*K1**3*K3*K4 - 416*K1**3*K3 - 2176*K1**2*K2**2 - 384*K1**2*K2*K4 + 6896*K1**2*K2 - 2016*K1**2*K3**2 - 128*K1**2*K3*K5 - 560*K1**2*K4**2 - 32*K1**2*K4*K6 - 4516*K1**2 - 256*K1*K2**2*K3 - 160*K1*K2*K3*K4 + 6032*K1*K2*K3 + 3920*K1*K3*K4 + 952*K1*K4*K5 + 72*K1*K5*K6 - 88*K2**4 - 144*K2**2*K3**2 - 16*K2**2*K4**2 + 584*K2**2*K4 - 3884*K2**2 + 360*K2*K3*K5 + 72*K2*K4*K6 - 3044*K3**2 - 1694*K4**2 - 432*K5**2 - 60*K6**2 + 5084 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {2, 5}, {3, 4}], [{1, 6}, {5}, {3, 4}, {2}], [{3, 6}, {2, 5}, {1, 4}], [{4, 6}, {2, 5}, {1, 3}], [{5, 6}, {2, 4}, {1, 3}], [{5, 6}, {2, 4}, {3}, {1}]] |
| If K is slice | False |