| Min(phi) over symmetries of the knot is: [-2,-1,0,0,1,2,-1,1,1,2,2,0,1,1,1,1,1,2,2,1,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.1028'] |
| Arrow polynomial of the knot is: 8*K1**3 - 4*K1**2 - 4*K1*K2 - 4*K1 + 2*K2 + 3 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.206', '6.236', '6.575', '6.580', '6.613', '6.619', '6.810', '6.819', '6.831', '6.838', '6.957', '6.1018', '6.1028', '6.1046', '6.1073', '6.1279', '6.1507', '6.1532', '6.1556', '6.1639', '6.1688', '6.1924', '6.1931'] |
| Outer characteristic polynomial of the knot is: t^7+35t^5+100t^3+21t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1028'] |
| 2-strand cable arrow polynomial of the knot is: -192*K1**4*K2**2 + 352*K1**4*K2 - 688*K1**4 + 160*K1**3*K2*K3 - 64*K1**3*K3 - 128*K1**2*K2**4 + 2112*K1**2*K2**3 - 6272*K1**2*K2**2 - 448*K1**2*K2*K4 + 5496*K1**2*K2 - 16*K1**2*K3**2 - 3540*K1**2 + 896*K1*K2**3*K3 - 800*K1*K2**2*K3 - 96*K1*K2**2*K5 - 160*K1*K2*K3*K4 + 4560*K1*K2*K3 + 184*K1*K3*K4 + 8*K1*K4*K5 - 448*K2**6 + 544*K2**4*K4 - 2944*K2**4 - 96*K2**3*K6 - 688*K2**2*K3**2 - 112*K2**2*K4**2 + 1888*K2**2*K4 - 1160*K2**2 + 264*K2*K3*K5 + 24*K2*K4*K6 - 936*K3**2 - 280*K4**2 - 4*K5**2 + 2582 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1028'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.10129', 'vk6.10178', 'vk6.10321', 'vk6.10416', 'vk6.17673', 'vk6.17720', 'vk6.24240', 'vk6.24284', 'vk6.29912', 'vk6.29951', 'vk6.30014', 'vk6.30071', 'vk6.36506', 'vk6.36602', 'vk6.43609', 'vk6.43713', 'vk6.51613', 'vk6.51642', 'vk6.51683', 'vk6.51714', 'vk6.55707', 'vk6.55766', 'vk6.60281', 'vk6.60339', 'vk6.63330', 'vk6.63345', 'vk6.63374', 'vk6.63393', 'vk6.65411', 'vk6.65452', 'vk6.68553', 'vk6.68583'] |
| 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 | O1O2O3O4U3U5O6U4O5U1U2U6 |
| R3 orbit | {'O1O2O3O4U3U5O6U4O5U1U2U6'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U5U3U4O6U1O5U6U2 |
| Gauss code of K* | O1O2O3U1U2U4U5O4O6U3O5U6 |
| Gauss code of -K* | O1O2O3U4O5U1O4O6U5U6U2U3 |
| 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 0 -1 1 0 2],[ 2 0 1 -1 2 1 2],[ 0 -1 0 -1 2 -1 1],[ 1 1 1 0 1 0 1],[-1 -2 -2 -1 0 -1 0],[ 0 -1 1 0 1 0 2],[-2 -2 -1 -1 0 -2 0]] |
| Primitive based matrix | [[ 0 2 1 0 0 -1 -2],[-2 0 0 -1 -2 -1 -2],[-1 0 0 -2 -1 -1 -2],[ 0 1 2 0 -1 -1 -1],[ 0 2 1 1 0 0 -1],[ 1 1 1 1 0 0 1],[ 2 2 2 1 1 -1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,0,0,1,2,0,1,2,1,2,2,1,1,2,1,1,1,0,1,-1] |
| Phi over symmetry | [-2,-1,0,0,1,2,-1,1,1,2,2,0,1,1,1,1,1,2,2,1,0] |
| Phi of -K | [-2,-1,0,0,1,2,2,1,1,1,2,0,1,1,2,1,-1,1,0,0,1] |
| Phi of K* | [-2,-1,0,0,1,2,1,0,1,2,2,0,-1,1,1,1,1,1,0,1,2] |
| Phi of -K* | [-2,-1,0,0,1,2,-1,1,1,2,2,0,1,1,1,1,1,2,2,1,0] |
| Symmetry type of based matrix | c |
| u-polynomial | 0 |
| Normalized Jones-Krushkal polynomial | 5z^2+22z+25 |
| Enhanced Jones-Krushkal polynomial | -2w^4z^2+7w^3z^2-4w^3z+26w^2z+25w |
| Inner characteristic polynomial | t^6+25t^4+48t^2+9 |
| Outer characteristic polynomial | t^7+35t^5+100t^3+21t |
| Flat arrow polynomial | 8*K1**3 - 4*K1**2 - 4*K1*K2 - 4*K1 + 2*K2 + 3 |
| 2-strand cable arrow polynomial | -192*K1**4*K2**2 + 352*K1**4*K2 - 688*K1**4 + 160*K1**3*K2*K3 - 64*K1**3*K3 - 128*K1**2*K2**4 + 2112*K1**2*K2**3 - 6272*K1**2*K2**2 - 448*K1**2*K2*K4 + 5496*K1**2*K2 - 16*K1**2*K3**2 - 3540*K1**2 + 896*K1*K2**3*K3 - 800*K1*K2**2*K3 - 96*K1*K2**2*K5 - 160*K1*K2*K3*K4 + 4560*K1*K2*K3 + 184*K1*K3*K4 + 8*K1*K4*K5 - 448*K2**6 + 544*K2**4*K4 - 2944*K2**4 - 96*K2**3*K6 - 688*K2**2*K3**2 - 112*K2**2*K4**2 + 1888*K2**2*K4 - 1160*K2**2 + 264*K2*K3*K5 + 24*K2*K4*K6 - 936*K3**2 - 280*K4**2 - 4*K5**2 + 2582 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {2, 5}, {3, 4}], [{2, 6}, {4, 5}, {1, 3}], [{4, 6}, {1, 5}, {2, 3}], [{4, 6}, {1, 5}, {3}, {2}]] |
| If K is slice | False |