| Min(phi) over symmetries of the knot is: [-3,-2,0,0,2,3,0,1,1,3,2,0,2,3,3,0,0,1,2,1,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.621'] |
| Arrow polynomial of the knot is: -4*K1**2 - 4*K1*K2 + 2*K1 + 2*K2 + 2*K3 + 3 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.65', '6.137', '6.201', '6.203', '6.214', '6.310', '6.314', '6.332', '6.385', '6.386', '6.401', '6.516', '6.564', '6.571', '6.572', '6.578', '6.621', '6.626', '6.716', '6.773', '6.807', '6.814', '6.821', '6.940', '6.966', '6.1036', '6.1071', '6.1108', '6.1111', '6.1131', '6.1188', '6.1203', '6.1206', '6.1220', '6.1340', '6.1387', '6.1548', '6.1663', '6.1680', '6.1693', '6.1831', '6.1932'] |
| Outer characteristic polynomial of the knot is: t^7+77t^5+333t^3 |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.621'] |
| 2-strand cable arrow polynomial of the knot is: -224*K1**2*K2**2 + 304*K1**2*K2 - 992*K1**2*K3**2 - 2312*K1**2 + 64*K1*K2*K3**3 + 4128*K1*K2*K3 + 1216*K1*K3*K4 + 32*K1*K4*K5 + 48*K1*K5*K6 - 16*K2**4 - 256*K2**2*K3**2 - 16*K2**2*K4**2 + 208*K2**2*K4 - 2124*K2**2 + 352*K2*K3*K5 + 32*K2*K4*K6 - 160*K3**4 + 80*K3**2*K6 - 2120*K3**2 - 492*K4**2 - 160*K5**2 - 44*K6**2 + 2450 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.621'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.73336', 'vk6.73499', 'vk6.75259', 'vk6.75507', 'vk6.78224', 'vk6.78467', 'vk6.80049', 'vk6.80199', 'vk6.81943', 'vk6.82188', 'vk6.82207', 'vk6.82672', 'vk6.84736', 'vk6.85036', 'vk6.85759', 'vk6.86508', 'vk6.87330', 'vk6.87694', 'vk6.89633', 'vk6.90079'] |
| The R3 orbit of minmal crossing diagrams contains: |
| The diagrammatic symmetry type of this knot is -. |
| The reverse -K is |
| The 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 | O1O2O3O4U5O6U2O5U1U3U6U4 |
| R3 orbit | {'O1O2O3O4U5O6U2O5U1U3U6U4'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U1U5U2U4O6U3O5U6 |
| Gauss code of K* | O1O2O3O4U1U5U2U4O6U3O5U6 |
| Gauss code of -K* | Same |
| Diagrammatic symmetry type | - |
| Flat genus of the diagram | 2 |
| If K is checkerboard colorable | False |
| If K is almost classical | False |
| Based matrix from Gauss code | [[ 0 -3 -2 0 3 0 2],[ 3 0 1 2 4 2 2],[ 2 -1 0 0 2 2 1],[ 0 -2 0 0 2 0 0],[-3 -4 -2 -2 0 -2 -1],[ 0 -2 -2 0 2 0 2],[-2 -2 -1 0 1 -2 0]] |
| Primitive based matrix | [[ 0 3 2 0 0 -2 -3],[-3 0 -1 -2 -2 -2 -4],[-2 1 0 0 -2 -1 -2],[ 0 2 0 0 0 0 -2],[ 0 2 2 0 0 -2 -2],[ 2 2 1 0 2 0 -1],[ 3 4 2 2 2 1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-3,-2,0,0,2,3,1,2,2,2,4,0,2,1,2,0,0,2,2,2,1] |
| Phi over symmetry | [-3,-2,0,0,2,3,0,1,1,3,2,0,2,3,3,0,0,1,2,1,0] |
| Phi of -K | [-3,-2,0,0,2,3,0,1,1,3,2,0,2,3,3,0,0,1,2,1,0] |
| Phi of K* | [-3,-2,0,0,2,3,0,1,1,3,2,0,2,3,3,0,0,1,2,1,0] |
| Phi of -K* | [-3,-2,0,0,2,3,1,2,2,2,4,0,2,1,2,0,0,2,2,2,1] |
| Symmetry type of based matrix | - |
| u-polynomial | 0 |
| Normalized Jones-Krushkal polynomial | 12z+25 |
| Enhanced Jones-Krushkal polynomial | -6w^3z+18w^2z+25w |
| Inner characteristic polynomial | t^6+51t^4+185t^2 |
| Outer characteristic polynomial | t^7+77t^5+333t^3 |
| Flat arrow polynomial | -4*K1**2 - 4*K1*K2 + 2*K1 + 2*K2 + 2*K3 + 3 |
| 2-strand cable arrow polynomial | -224*K1**2*K2**2 + 304*K1**2*K2 - 992*K1**2*K3**2 - 2312*K1**2 + 64*K1*K2*K3**3 + 4128*K1*K2*K3 + 1216*K1*K3*K4 + 32*K1*K4*K5 + 48*K1*K5*K6 - 16*K2**4 - 256*K2**2*K3**2 - 16*K2**2*K4**2 + 208*K2**2*K4 - 2124*K2**2 + 352*K2*K3*K5 + 32*K2*K4*K6 - 160*K3**4 + 80*K3**2*K6 - 2120*K3**2 - 492*K4**2 - 160*K5**2 - 44*K6**2 + 2450 |
| Genus of based matrix | 0 |
| Fillings of based matrix | [[{2, 6}, {3, 5}, {1, 4}], [{2, 6}, {5}, {1, 4}, {3}]] |
| If K is slice | True |