| Min(phi) over symmetries of the knot is: [-2,-1,0,0,1,2,0,0,1,3,3,2,2,1,1,1,0,0,1,1,1] |
| Flat knots (up to 7 crossings) with same phi are :['6.1507'] |
| 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+31t^5+92t^3+16t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1507'] |
| 2-strand cable arrow polynomial of the knot is: -384*K1**4*K2**2 + 608*K1**4*K2 - 720*K1**4 + 224*K1**3*K2*K3 - 96*K1**3*K3 - 128*K1**2*K2**4 + 1344*K1**2*K2**3 - 5952*K1**2*K2**2 - 352*K1**2*K2*K4 + 5040*K1**2*K2 - 80*K1**2*K3**2 - 3164*K1**2 + 1088*K1*K2**3*K3 - 736*K1*K2**2*K3 - 224*K1*K2**2*K5 - 96*K1*K2*K3*K4 + 5192*K1*K2*K3 + 208*K1*K3*K4 + 8*K1*K4*K5 - 448*K2**6 + 544*K2**4*K4 - 3328*K2**4 - 1232*K2**2*K3**2 - 208*K2**2*K4**2 + 2248*K2**2*K4 - 1104*K2**2 + 696*K2*K3*K5 + 24*K2*K4*K6 - 1152*K3**2 - 332*K4**2 - 92*K5**2 + 2602 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1507'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.11451', 'vk6.11748', 'vk6.12766', 'vk6.13108', 'vk6.20675', 'vk6.22114', 'vk6.28180', 'vk6.29604', 'vk6.31205', 'vk6.31544', 'vk6.32373', 'vk6.32786', 'vk6.39631', 'vk6.41872', 'vk6.46235', 'vk6.47842', 'vk6.52213', 'vk6.52486', 'vk6.53048', 'vk6.53368', 'vk6.57605', 'vk6.58766', 'vk6.62265', 'vk6.63208', 'vk6.63780', 'vk6.63893', 'vk6.64210', 'vk6.64394', 'vk6.67067', 'vk6.67933', 'vk6.69683', 'vk6.70365'] |
| 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 | O1O2O3U2O4U1U3O5O6U4U5U6 |
| R3 orbit | {'O1O2O3U2O4U1U3O5O6U4U5U6'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U4U5U6O4O5U1U3O6U2 |
| Gauss code of K* | O1O2O3U4U5U6O5U1O4O6U2U3 |
| Gauss code of -K* | O1O2O3U1U2O4O5U3O6U4U6U5 |
| 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 1 0 0 2],[ 2 0 0 2 2 1 1],[ 1 0 0 1 1 0 0],[-1 -2 -1 0 1 1 1],[ 0 -2 -1 -1 0 1 2],[ 0 -1 0 -1 -1 0 1],[-2 -1 0 -1 -2 -1 0]] |
| Primitive based matrix | [[ 0 2 1 0 0 -1 -2],[-2 0 -1 -1 -2 0 -1],[-1 1 0 1 1 -1 -2],[ 0 1 -1 0 -1 0 -1],[ 0 2 -1 1 0 -1 -2],[ 1 0 1 0 1 0 0],[ 2 1 2 1 2 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,0,0,1,2,1,1,2,0,1,-1,-1,1,2,1,0,1,1,2,0] |
| Phi over symmetry | [-2,-1,0,0,1,2,0,0,1,3,3,2,2,1,1,1,0,0,1,1,1] |
| Phi of -K | [-2,-1,0,0,1,2,1,0,1,1,3,0,1,1,3,-1,2,0,2,1,0] |
| Phi of K* | [-2,-1,0,0,1,2,0,0,1,3,3,2,2,1,1,1,0,0,1,1,1] |
| Phi of -K* | [-2,-1,0,0,1,2,0,1,2,2,1,0,1,1,0,-1,-1,1,-1,2,1] |
| Symmetry type of based matrix | c |
| u-polynomial | 0 |
| Normalized Jones-Krushkal polynomial | 3z^2+16z+21 |
| Enhanced Jones-Krushkal polynomial | -2w^4z^2+5w^3z^2-8w^3z+24w^2z+21w |
| Inner characteristic polynomial | t^6+21t^4+22t^2+1 |
| Outer characteristic polynomial | t^7+31t^5+92t^3+16t |
| Flat arrow polynomial | 8*K1**3 - 4*K1**2 - 4*K1*K2 - 4*K1 + 2*K2 + 3 |
| 2-strand cable arrow polynomial | -384*K1**4*K2**2 + 608*K1**4*K2 - 720*K1**4 + 224*K1**3*K2*K3 - 96*K1**3*K3 - 128*K1**2*K2**4 + 1344*K1**2*K2**3 - 5952*K1**2*K2**2 - 352*K1**2*K2*K4 + 5040*K1**2*K2 - 80*K1**2*K3**2 - 3164*K1**2 + 1088*K1*K2**3*K3 - 736*K1*K2**2*K3 - 224*K1*K2**2*K5 - 96*K1*K2*K3*K4 + 5192*K1*K2*K3 + 208*K1*K3*K4 + 8*K1*K4*K5 - 448*K2**6 + 544*K2**4*K4 - 3328*K2**4 - 1232*K2**2*K3**2 - 208*K2**2*K4**2 + 2248*K2**2*K4 - 1104*K2**2 + 696*K2*K3*K5 + 24*K2*K4*K6 - 1152*K3**2 - 332*K4**2 - 92*K5**2 + 2602 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {4, 5}, {2, 3}]] |
| If K is slice | False |