| Min(phi) over symmetries of the knot is: [-2,-2,-1,1,2,2,-2,-1,2,3,3,0,2,1,2,2,1,2,1,1,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.887'] |
| 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+49t^5+73t^3+5t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.887'] |
| 2-strand cable arrow polynomial of the knot is: -192*K1**2*K2**4 + 736*K1**2*K2**3 + 128*K1**2*K2**2*K4 - 3600*K1**2*K2**2 - 224*K1**2*K2*K4 + 3840*K1**2*K2 - 64*K1**2*K3**2 - 64*K1**2*K4**2 - 3832*K1**2 + 480*K1*K2**3*K3 - 896*K1*K2**2*K3 - 128*K1*K2**2*K5 + 32*K1*K2*K3**3 - 448*K1*K2*K3*K4 - 32*K1*K2*K3*K6 + 5552*K1*K2*K3 + 944*K1*K3*K4 + 200*K1*K4*K5 - 32*K2**6 + 64*K2**4*K4 - 1120*K2**4 - 848*K2**2*K3**2 - 112*K2**2*K4**2 + 1536*K2**2*K4 - 3006*K2**2 - 160*K2*K3**2*K4 + 856*K2*K3*K5 + 144*K2*K4*K6 - 64*K3**4 + 120*K3**2*K6 - 2120*K3**2 - 740*K4**2 - 216*K5**2 - 50*K6**2 + 3314 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.887'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.4733', 'vk6.5057', 'vk6.6265', 'vk6.6710', 'vk6.8230', 'vk6.8675', 'vk6.9617', 'vk6.9939', 'vk6.20656', 'vk6.22087', 'vk6.28142', 'vk6.29571', 'vk6.39584', 'vk6.41815', 'vk6.46199', 'vk6.47817', 'vk6.48765', 'vk6.48971', 'vk6.49569', 'vk6.49780', 'vk6.50775', 'vk6.50984', 'vk6.51257', 'vk6.51461', 'vk6.57580', 'vk6.58746', 'vk6.62250', 'vk6.63196', 'vk6.67050', 'vk6.67923', 'vk6.69675', 'vk6.70356'] |
| 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 | O1O2O3O4U2U1O5O6U5U4U6U3 |
| R3 orbit | {'O1O2O3O4U2U1O5O6U5U4U6U3'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U2U5U1U6O5O6U4U3 |
| Gauss code of K* | O1O2O3O4U5U6U4U2O6O5U1U3 |
| Gauss code of -K* | O1O2O3O4U2U4O5O6U3U1U6U5 |
| 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 -2 2 1 -1 2],[ 2 0 0 3 2 0 1],[ 2 0 0 2 1 0 1],[-2 -3 -2 0 -1 -1 2],[-1 -2 -1 1 0 0 2],[ 1 0 0 1 0 0 1],[-2 -1 -1 -2 -2 -1 0]] |
| Primitive based matrix | [[ 0 2 2 1 -1 -2 -2],[-2 0 2 -1 -1 -2 -3],[-2 -2 0 -2 -1 -1 -1],[-1 1 2 0 0 -1 -2],[ 1 1 1 0 0 0 0],[ 2 2 1 1 0 0 0],[ 2 3 1 2 0 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-2,-1,1,2,2,-2,1,1,2,3,2,1,1,1,0,1,2,0,0,0] |
| Phi over symmetry | [-2,-2,-1,1,2,2,-2,-1,2,3,3,0,2,1,2,2,1,2,1,1,0] |
| Phi of -K | [-2,-2,-1,1,2,2,0,1,1,1,3,1,2,2,3,2,2,2,0,-1,-2] |
| Phi of K* | [-2,-2,-1,1,2,2,-2,-1,2,3,3,0,2,1,2,2,1,2,1,1,0] |
| Phi of -K* | [-2,-2,-1,1,2,2,0,0,1,1,2,0,2,1,3,0,1,1,2,1,-2] |
| Symmetry type of based matrix | c |
| u-polynomial | 0 |
| Normalized Jones-Krushkal polynomial | 8z^2+27z+23 |
| Enhanced Jones-Krushkal polynomial | 8w^3z^2+27w^2z+23w |
| Inner characteristic polynomial | t^6+31t^4+21t^2 |
| Outer characteristic polynomial | t^7+49t^5+73t^3+5t |
| Flat arrow polynomial | 4*K1**3 - 4*K1*K2 - K1 + K3 + 1 |
| 2-strand cable arrow polynomial | -192*K1**2*K2**4 + 736*K1**2*K2**3 + 128*K1**2*K2**2*K4 - 3600*K1**2*K2**2 - 224*K1**2*K2*K4 + 3840*K1**2*K2 - 64*K1**2*K3**2 - 64*K1**2*K4**2 - 3832*K1**2 + 480*K1*K2**3*K3 - 896*K1*K2**2*K3 - 128*K1*K2**2*K5 + 32*K1*K2*K3**3 - 448*K1*K2*K3*K4 - 32*K1*K2*K3*K6 + 5552*K1*K2*K3 + 944*K1*K3*K4 + 200*K1*K4*K5 - 32*K2**6 + 64*K2**4*K4 - 1120*K2**4 - 848*K2**2*K3**2 - 112*K2**2*K4**2 + 1536*K2**2*K4 - 3006*K2**2 - 160*K2*K3**2*K4 + 856*K2*K3*K5 + 144*K2*K4*K6 - 64*K3**4 + 120*K3**2*K6 - 2120*K3**2 - 740*K4**2 - 216*K5**2 - 50*K6**2 + 3314 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {4, 5}, {2, 3}], [{2, 6}, {4, 5}, {1, 3}]] |
| If K is slice | False |