| Min(phi) over symmetries of the knot is: [-3,-1,0,0,1,3,1,0,1,2,4,-1,0,0,2,0,-1,0,0,1,1] |
| Flat knots (up to 7 crossings) with same phi are :['6.578'] |
| 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+74t^5+69t^3 |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.578'] |
| 2-strand cable arrow polynomial of the knot is: -32*K1**4 - 864*K1**2*K2**2 + 592*K1**2*K2 - 64*K1**2*K3**2 - 896*K1**2 + 384*K1*K2**3*K3 + 1856*K1*K2*K3 + 96*K1*K3*K4 - 560*K2**4 - 608*K2**2*K3**2 - 16*K2**2*K4**2 + 208*K2**2*K4 - 460*K2**2 + 320*K2*K3*K5 + 16*K2*K4*K6 - 32*K3**4 + 16*K3**2*K6 - 712*K3**2 - 44*K4**2 - 56*K5**2 - 4*K6**2 + 858 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.578'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.73756', 'vk6.73894', 'vk6.75702', 'vk6.75895', 'vk6.78687', 'vk6.78884', 'vk6.80311', 'vk6.80435', 'vk6.81108', 'vk6.81110', 'vk6.81133', 'vk6.81229', 'vk6.81232', 'vk6.81804', 'vk6.82203', 'vk6.82471', 'vk6.84007', 'vk6.84448', 'vk6.86338', 'vk6.87775', 'vk6.87904', 'vk6.88108', 'vk6.88401', 'vk6.88564', 'vk6.88569', 'vk6.90048'] |
| 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 | O1O2O3O4U1O5U3O6U4U5U2U6 |
| R3 orbit | {'O1O2O3O4U1U2O5O6U4U3U5U6', 'O1O2O3O4U1O5U3O6U4U5U2U6'} |
| R3 orbit length | 2 |
| Gauss code of -K | O1O2O3O4U5U3U6U1O5U2O6U4 |
| Gauss code of K* | O1O2O3O4U5U3U6U1O5U2O6U4 |
| 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 0 -1 0 1 3],[ 3 0 3 1 2 2 2],[ 0 -3 0 -2 0 2 3],[ 1 -1 2 0 1 2 2],[ 0 -2 0 -1 0 1 2],[-1 -2 -2 -2 -1 0 1],[-3 -2 -3 -2 -2 -1 0]] |
| Primitive based matrix | [[ 0 3 1 0 0 -1 -3],[-3 0 -1 -2 -3 -2 -2],[-1 1 0 -1 -2 -2 -2],[ 0 2 1 0 0 -1 -2],[ 0 3 2 0 0 -2 -3],[ 1 2 2 1 2 0 -1],[ 3 2 2 2 3 1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-3,-1,0,0,1,3,1,2,3,2,2,1,2,2,2,0,1,2,2,3,1] |
| Phi over symmetry | [-3,-1,0,0,1,3,1,0,1,2,4,-1,0,0,2,0,-1,0,0,1,1] |
| Phi of -K | [-3,-1,0,0,1,3,1,0,1,2,4,-1,0,0,2,0,-1,0,0,1,1] |
| Phi of K* | [-3,-1,0,0,1,3,1,0,1,2,4,-1,0,0,2,0,-1,0,0,1,1] |
| Phi of -K* | [-3,-1,0,0,1,3,1,2,3,2,2,1,2,2,2,0,1,2,2,3,1] |
| Symmetry type of based matrix | - |
| u-polynomial | 0 |
| Normalized Jones-Krushkal polynomial | 4z+9 |
| Enhanced Jones-Krushkal polynomial | 4w^4z-10w^3z+4w^3+10w^2z+5w |
| Inner characteristic polynomial | t^6+54t^4+9t^2 |
| Outer characteristic polynomial | t^7+74t^5+69t^3 |
| Flat arrow polynomial | -4*K1**2 - 4*K1*K2 + 2*K1 + 2*K2 + 2*K3 + 3 |
| 2-strand cable arrow polynomial | -32*K1**4 - 864*K1**2*K2**2 + 592*K1**2*K2 - 64*K1**2*K3**2 - 896*K1**2 + 384*K1*K2**3*K3 + 1856*K1*K2*K3 + 96*K1*K3*K4 - 560*K2**4 - 608*K2**2*K3**2 - 16*K2**2*K4**2 + 208*K2**2*K4 - 460*K2**2 + 320*K2*K3*K5 + 16*K2*K4*K6 - 32*K3**4 + 16*K3**2*K6 - 712*K3**2 - 44*K4**2 - 56*K5**2 - 4*K6**2 + 858 |
| Genus of based matrix | 0 |
| Fillings of based matrix | [[{1, 6}, {3, 5}, {2, 4}], [{1, 6}, {3, 5}, {4}, {2}]] |
| If K is slice | True |