| Min(phi) over symmetries of the knot is: [-2,-1,0,1,1,1,0,1,1,1,2,0,1,1,1,1,1,1,0,-1,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.1323'] |
| 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+22t^3+5t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1323'] |
| 2-strand cable arrow polynomial of the knot is: -128*K1**6 + 2880*K1**4*K2 - 6656*K1**4 + 512*K1**3*K2*K3 + 64*K1**3*K3*K4 - 2368*K1**3*K3 + 96*K1**2*K2**3 - 4448*K1**2*K2**2 - 672*K1**2*K2*K4 + 11032*K1**2*K2 - 1024*K1**2*K3**2 - 368*K1**2*K4**2 - 5128*K1**2 - 480*K1*K2**2*K3 - 192*K1*K2*K3*K4 + 6760*K1*K2*K3 + 1928*K1*K3*K4 + 400*K1*K4*K5 - 88*K2**4 - 64*K2**2*K3**2 - 48*K2**2*K4**2 + 520*K2**2*K4 - 4460*K2**2 + 128*K2*K3*K5 + 32*K2*K4*K6 - 2156*K3**2 - 718*K4**2 - 116*K5**2 - 4*K6**2 + 4764 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1323'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.4823', 'vk6.5167', 'vk6.6384', 'vk6.6815', 'vk6.8353', 'vk6.8785', 'vk6.9721', 'vk6.10025', 'vk6.11621', 'vk6.11972', 'vk6.12963', 'vk6.20473', 'vk6.20738', 'vk6.21826', 'vk6.27857', 'vk6.29365', 'vk6.31432', 'vk6.32606', 'vk6.39295', 'vk6.39770', 'vk6.41473', 'vk6.46330', 'vk6.47592', 'vk6.47905', 'vk6.49049', 'vk6.49873', 'vk6.51307', 'vk6.51525', 'vk6.53212', 'vk6.57332', 'vk6.62018', 'vk6.64301'] |
| 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 | O1O2O3U4O5O6U3U6O4U1U5U2 |
| R3 orbit | {'O1O2O3U4O5O6U3U6O4U1U5U2'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U2U4U3O5U6U1O6O4U5 |
| Gauss code of K* | O1O2O3U1U3U4O5U2U6O4O6U5 |
| Gauss code of -K* | O1O2O3U4O5O6U5U2O4U6U1U3 |
| 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 2 0 1 1 1],[-1 -2 0 -1 -1 0 1],[ 1 0 1 0 0 1 1],[ 0 -1 1 0 0 1 1],[-1 -1 0 -1 -1 0 0],[-1 -1 -1 -1 -1 0 0]] |
| Primitive based matrix | [[ 0 1 1 1 0 -1 -2],[-1 0 1 0 -1 -1 -2],[-1 -1 0 0 -1 -1 -1],[-1 0 0 0 -1 -1 -1],[ 0 1 1 1 0 0 -1],[ 1 1 1 1 0 0 0],[ 2 2 1 1 1 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-1,-1,-1,0,1,2,-1,0,1,1,2,0,1,1,1,1,1,1,0,1,0] |
| Phi over symmetry | [-2,-1,0,1,1,1,0,1,1,1,2,0,1,1,1,1,1,1,0,-1,0] |
| Phi of -K | [-2,-1,0,1,1,1,1,1,1,2,2,1,1,1,1,0,0,0,-1,0,0] |
| Phi of K* | [-1,-1,-1,0,1,2,-1,0,0,1,2,0,0,1,1,0,1,2,1,1,1] |
| Phi of -K* | [-2,-1,0,1,1,1,0,1,1,1,2,0,1,1,1,1,1,1,0,-1,0] |
| Symmetry type of based matrix | c |
| u-polynomial | t^2-2t |
| Normalized Jones-Krushkal polynomial | 3z^2+24z+37 |
| Enhanced Jones-Krushkal polynomial | 3w^3z^2+24w^2z+37w |
| Inner characteristic polynomial | t^6+14t^4+9t^2+1 |
| Outer characteristic polynomial | t^7+22t^5+22t^3+5t |
| Flat arrow polynomial | -6*K1**2 - 4*K1*K2 + 2*K1 + 3*K2 + 2*K3 + 4 |
| 2-strand cable arrow polynomial | -128*K1**6 + 2880*K1**4*K2 - 6656*K1**4 + 512*K1**3*K2*K3 + 64*K1**3*K3*K4 - 2368*K1**3*K3 + 96*K1**2*K2**3 - 4448*K1**2*K2**2 - 672*K1**2*K2*K4 + 11032*K1**2*K2 - 1024*K1**2*K3**2 - 368*K1**2*K4**2 - 5128*K1**2 - 480*K1*K2**2*K3 - 192*K1*K2*K3*K4 + 6760*K1*K2*K3 + 1928*K1*K3*K4 + 400*K1*K4*K5 - 88*K2**4 - 64*K2**2*K3**2 - 48*K2**2*K4**2 + 520*K2**2*K4 - 4460*K2**2 + 128*K2*K3*K5 + 32*K2*K4*K6 - 2156*K3**2 - 718*K4**2 - 116*K5**2 - 4*K6**2 + 4764 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {3, 5}, {2, 4}], [{1, 6}, {4, 5}, {2, 3}], [{2, 6}, {3, 5}, {1, 4}], [{4, 6}, {1, 5}, {2, 3}], [{4, 6}, {3, 5}, {1, 2}], [{5, 6}, {1, 4}, {2, 3}]] |
| If K is slice | False |