| Min(phi) over symmetries of the knot is: [-2,-1,0,0,1,2,-1,1,2,1,1,0,0,0,1,0,0,1,0,2,-1] |
| Flat knots (up to 7 crossings) with same phi are :['6.1693'] |
| 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+45t^5+154t^3 |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1693'] |
| 2-strand cable arrow polynomial of the knot is: -416*K1**4 + 640*K1**3*K2*K3 - 1216*K1**2*K2**2 + 784*K1**2*K2 - 1504*K1**2*K3**2 - 32*K1**2*K5**2 - 1736*K1**2 + 4112*K1*K2*K3 + 1072*K1*K3*K4 + 48*K1*K4*K5 + 80*K1*K5*K6 - 16*K2**4 - 32*K2**2*K3**2 - 16*K2**2*K4**2 + 144*K2**2*K4 - 1860*K2**2 + 128*K2*K3*K5 + 32*K2*K4*K6 - 1824*K3**2 - 332*K4**2 - 104*K5**2 - 44*K6**2 + 2090 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1693'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.14111', 'vk6.14326', 'vk6.15555', 'vk6.16033', 'vk6.16437', 'vk6.16448', 'vk6.22847', 'vk6.34062', 'vk6.34124', 'vk6.34461', 'vk6.34498', 'vk6.34791', 'vk6.34812', 'vk6.42410', 'vk6.54084', 'vk6.54316', 'vk6.54666', 'vk6.54687', 'vk6.64542', 'vk6.64734'] |
| 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 | O1O2O3U4O5U3U2U6O4O6U1U5 |
| R3 orbit | {'O1O2O3U4O5U3U2U6O4O6U1U5'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U4U3O5O6U5U2U1O4U6 |
| Gauss code of K* | O1O2O3U4U3O5O6U5U2U1O4U6 |
| 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 -1 0 0 -2 2 1],[ 1 0 1 1 -2 2 2],[ 0 -1 0 0 -1 1 1],[ 0 -1 0 0 0 0 1],[ 2 2 1 0 0 3 2],[-2 -2 -1 0 -3 0 -2],[-1 -2 -1 -1 -2 2 0]] |
| Primitive based matrix | [[ 0 2 1 0 0 -1 -2],[-2 0 -2 0 -1 -2 -3],[-1 2 0 -1 -1 -2 -2],[ 0 0 1 0 0 -1 0],[ 0 1 1 0 0 -1 -1],[ 1 2 2 1 1 0 -2],[ 2 3 2 0 1 2 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,0,0,1,2,2,0,1,2,3,1,1,2,2,0,1,0,1,1,2] |
| Phi over symmetry | [-2,-1,0,0,1,2,-1,1,2,1,1,0,0,0,1,0,0,1,0,2,-1] |
| Phi of -K | [-2,-1,0,0,1,2,-1,1,2,1,1,0,0,0,1,0,0,1,0,2,-1] |
| Phi of K* | [-2,-1,0,0,1,2,-1,1,2,1,1,0,0,0,1,0,0,1,0,2,-1] |
| Phi of -K* | [-2,-1,0,0,1,2,2,0,1,2,3,1,1,2,2,0,1,0,1,1,2] |
| Symmetry type of based matrix | - |
| u-polynomial | 0 |
| Normalized Jones-Krushkal polynomial | 10z+21 |
| Enhanced Jones-Krushkal polynomial | -10w^3z+20w^2z+21w |
| Inner characteristic polynomial | t^6+35t^4+116t^2 |
| Outer characteristic polynomial | t^7+45t^5+154t^3 |
| Flat arrow polynomial | -4*K1**2 - 4*K1*K2 + 2*K1 + 2*K2 + 2*K3 + 3 |
| 2-strand cable arrow polynomial | -416*K1**4 + 640*K1**3*K2*K3 - 1216*K1**2*K2**2 + 784*K1**2*K2 - 1504*K1**2*K3**2 - 32*K1**2*K5**2 - 1736*K1**2 + 4112*K1*K2*K3 + 1072*K1*K3*K4 + 48*K1*K4*K5 + 80*K1*K5*K6 - 16*K2**4 - 32*K2**2*K3**2 - 16*K2**2*K4**2 + 144*K2**2*K4 - 1860*K2**2 + 128*K2*K3*K5 + 32*K2*K4*K6 - 1824*K3**2 - 332*K4**2 - 104*K5**2 - 44*K6**2 + 2090 |
| Genus of based matrix | 0 |
| Fillings of based matrix | [[{1, 6}, {4, 5}, {2, 3}], [{1, 6}, {4, 5}, {3}, {2}]] |
| If K is slice | True |