| Min(phi) over symmetries of the knot is: [-2,-2,1,1,1,1,-2,1,1,1,2,0,1,2,2,0,0,0,0,-1,-1] |
| Flat knots (up to 7 crossings) with same phi are :['6.548'] |
| Arrow polynomial of the knot is: 4*K1**3 - 4*K1*K2 - K1 + K3 + 1 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.395', '6.430', '6.440', '6.548', '6.551', '6.774', '6.832', '6.887', '6.908', '6.911', '6.1205', '6.1332', '6.1339', '6.1341', '6.1346', '6.1382', '6.1488', '6.1651', '6.1655', '6.1686'] |
| Outer characteristic polynomial of the knot is: t^7+34t^5+77t^3+8t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.548', '6.565'] |
| 2-strand cable arrow polynomial of the knot is: 1792*K1**4*K2 - 3264*K1**4 - 384*K1**3*K2**2*K3 + 1536*K1**3*K2*K3 - 1088*K1**3*K3 - 128*K1**2*K2**4 + 1344*K1**2*K2**3 - 128*K1**2*K2**2*K3**2 + 256*K1**2*K2**2*K4 - 7216*K1**2*K2**2 + 768*K1**2*K2*K3**2 - 544*K1**2*K2*K4 + 7088*K1**2*K2 - 2656*K1**2*K3**2 - 128*K1**2*K3*K5 - 32*K1**2*K4**2 - 2704*K1**2 + 1088*K1*K2**3*K3 + 64*K1*K2**2*K3*K4 - 2336*K1*K2**2*K3 - 288*K1*K2**2*K5 + 384*K1*K2*K3**3 - 704*K1*K2*K3*K4 - 128*K1*K2*K3*K6 + 7952*K1*K2*K3 + 2080*K1*K3*K4 + 96*K1*K4*K5 - 32*K2**6 + 64*K2**4*K4 - 1600*K2**4 - 1936*K2**2*K3**2 - 80*K2**2*K4**2 + 1664*K2**2*K4 - 2542*K2**2 - 128*K2*K3**2*K4 + 1216*K2*K3*K5 + 80*K2*K4*K6 - 288*K3**4 + 192*K3**2*K6 - 1652*K3**2 - 468*K4**2 - 124*K5**2 - 34*K6**2 + 2946 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.548'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.3257', 'vk6.3285', 'vk6.3293', 'vk6.3391', 'vk6.3418', 'vk6.3424', 'vk6.3464', 'vk6.3522', 'vk6.4614', 'vk6.5899', 'vk6.6028', 'vk6.7946', 'vk6.8069', 'vk6.9378', 'vk6.17851', 'vk6.17866', 'vk6.19052', 'vk6.19881', 'vk6.24372', 'vk6.25670', 'vk6.25685', 'vk6.26323', 'vk6.26766', 'vk6.37772', 'vk6.43789', 'vk6.43802', 'vk6.45068', 'vk6.48109', 'vk6.48120', 'vk6.48143', 'vk6.48200', 'vk6.50658'] |
| 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 | O1O2O3O4O5U3U5U4O6U1U6U2 |
| R3 orbit | {'O1O2O3O4O5U3U5U4O6U1U6U2'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4O5U4U6U5O6U2U1U3 |
| Gauss code of K* | O1O2O3U4O5O4O6U5U6U1U3U2 |
| Gauss code of -K* | O1O2O3U2O4O5O6U5U4U6U1U3 |
| 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 -2 1 1 1],[ 2 0 2 -2 1 1 1],[-1 -2 0 -2 1 1 0],[ 2 2 2 0 2 1 0],[-1 -1 -1 -2 0 0 0],[-1 -1 -1 -1 0 0 0],[-1 -1 0 0 0 0 0]] |
| Primitive based matrix | [[ 0 1 1 1 1 -2 -2],[-1 0 1 1 0 -2 -2],[-1 -1 0 0 0 -1 -1],[-1 -1 0 0 0 -1 -2],[-1 0 0 0 0 -1 0],[ 2 2 1 1 1 0 -2],[ 2 2 1 2 0 2 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-1,-1,-1,-1,2,2,-1,-1,0,2,2,0,0,1,1,0,1,2,1,0,2] |
| Phi over symmetry | [-2,-2,1,1,1,1,-2,1,1,1,2,0,1,2,2,0,0,0,0,-1,-1] |
| Phi of -K | [-2,-2,1,1,1,1,-2,1,1,2,3,1,2,2,2,-1,-1,0,0,0,0] |
| Phi of K* | [-1,-1,-1,-1,2,2,-1,0,0,1,2,0,1,1,1,0,3,2,2,2,2] |
| Phi of -K* | [-2,-2,1,1,1,1,-2,1,1,1,2,0,1,2,2,0,0,0,0,-1,-1] |
| Symmetry type of based matrix | c |
| u-polynomial | 2t^2-4t |
| Normalized Jones-Krushkal polynomial | 9z^2+30z+25 |
| Enhanced Jones-Krushkal polynomial | 9w^3z^2+30w^2z+25w |
| Inner characteristic polynomial | t^6+22t^4+33t^2+1 |
| Outer characteristic polynomial | t^7+34t^5+77t^3+8t |
| Flat arrow polynomial | 4*K1**3 - 4*K1*K2 - K1 + K3 + 1 |
| 2-strand cable arrow polynomial | 1792*K1**4*K2 - 3264*K1**4 - 384*K1**3*K2**2*K3 + 1536*K1**3*K2*K3 - 1088*K1**3*K3 - 128*K1**2*K2**4 + 1344*K1**2*K2**3 - 128*K1**2*K2**2*K3**2 + 256*K1**2*K2**2*K4 - 7216*K1**2*K2**2 + 768*K1**2*K2*K3**2 - 544*K1**2*K2*K4 + 7088*K1**2*K2 - 2656*K1**2*K3**2 - 128*K1**2*K3*K5 - 32*K1**2*K4**2 - 2704*K1**2 + 1088*K1*K2**3*K3 + 64*K1*K2**2*K3*K4 - 2336*K1*K2**2*K3 - 288*K1*K2**2*K5 + 384*K1*K2*K3**3 - 704*K1*K2*K3*K4 - 128*K1*K2*K3*K6 + 7952*K1*K2*K3 + 2080*K1*K3*K4 + 96*K1*K4*K5 - 32*K2**6 + 64*K2**4*K4 - 1600*K2**4 - 1936*K2**2*K3**2 - 80*K2**2*K4**2 + 1664*K2**2*K4 - 2542*K2**2 - 128*K2*K3**2*K4 + 1216*K2*K3*K5 + 80*K2*K4*K6 - 288*K3**4 + 192*K3**2*K6 - 1652*K3**2 - 468*K4**2 - 124*K5**2 - 34*K6**2 + 2946 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{4, 6}, {2, 5}, {1, 3}]] |
| If K is slice | False |