| Min(phi) over symmetries of the knot is: [-3,-3,1,1,2,2,-1,1,3,3,4,0,2,1,3,0,0,-1,0,0,-1] |
| Flat knots (up to 7 crossings) with same phi are :['6.819'] |
| 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+92t^5+94t^3+5t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.819'] |
| 2-strand cable arrow polynomial of the knot is: -64*K1**6 + 672*K1**4*K2 - 2304*K1**4 + 288*K1**3*K2*K3 + 32*K1**3*K3*K4 - 320*K1**3*K3 - 192*K1**2*K2**4 + 672*K1**2*K2**3 + 224*K1**2*K2**2*K4 - 4288*K1**2*K2**2 - 544*K1**2*K2*K4 + 6784*K1**2*K2 - 352*K1**2*K3**2 - 112*K1**2*K4**2 - 3884*K1**2 + 288*K1*K2**3*K3 + 64*K1*K2**2*K3*K4 - 960*K1*K2**2*K3 - 128*K1*K2**2*K5 - 32*K1*K2*K3*K4 + 4944*K1*K2*K3 - 32*K1*K2*K4*K5 + 680*K1*K3*K4 + 56*K1*K4*K5 - 64*K2**6 + 64*K2**4*K4 - 864*K2**4 - 352*K2**2*K3**2 - 48*K2**2*K4**2 + 880*K2**2*K4 - 2848*K2**2 + 160*K2*K3*K5 + 16*K2*K4*K6 - 1292*K3**2 - 232*K4**2 - 8*K5**2 + 3094 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.819'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.11540', 'vk6.11873', 'vk6.12886', 'vk6.13195', 'vk6.20345', 'vk6.21686', 'vk6.27645', 'vk6.29189', 'vk6.31315', 'vk6.31712', 'vk6.32469', 'vk6.32886', 'vk6.39075', 'vk6.41331', 'vk6.45827', 'vk6.47496', 'vk6.52315', 'vk6.52577', 'vk6.53155', 'vk6.53457', 'vk6.57216', 'vk6.58437', 'vk6.61826', 'vk6.62957', 'vk6.63816', 'vk6.63950', 'vk6.64258', 'vk6.64456', 'vk6.66825', 'vk6.67693', 'vk6.69461', 'vk6.70183'] |
| 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 | O1O2O3O4U1O5U6U4U5U3O6U2 |
| R3 orbit | {'O1O2O3O4U1O5U6U4U5U3O6U2'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U3O5U2U6U1U5O6U4 |
| Gauss code of K* | O1O2O3O4U1O5U6U5U4U2O6U3 |
| Gauss code of -K* | O1O2O3O4U2O5U3U1U6U5O6U4 |
| 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 -3 1 2 1 2 -3],[ 3 0 3 2 1 1 1],[-1 -3 0 1 0 2 -4],[-2 -2 -1 0 -1 1 -4],[-1 -1 0 1 0 1 -2],[-2 -1 -2 -1 -1 0 -2],[ 3 -1 4 4 2 2 0]] |
| Primitive based matrix | [[ 0 2 2 1 1 -3 -3],[-2 0 1 -1 -1 -2 -4],[-2 -1 0 -1 -2 -1 -2],[-1 1 1 0 0 -1 -2],[-1 1 2 0 0 -3 -4],[ 3 2 1 1 3 0 1],[ 3 4 2 2 4 -1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-2,-1,-1,3,3,-1,1,1,2,4,1,2,1,2,0,1,2,3,4,-1] |
| Phi over symmetry | [-3,-3,1,1,2,2,-1,1,3,3,4,0,2,1,3,0,0,-1,0,0,-1] |
| Phi of -K | [-3,-3,1,1,2,2,-1,1,3,3,4,0,2,1,3,0,0,-1,0,0,-1] |
| Phi of K* | [-2,-2,-1,-1,3,3,-1,-1,0,3,4,0,0,1,3,0,0,1,2,3,-1] |
| Phi of -K* | [-3,-3,1,1,2,2,-1,2,4,2,4,1,3,1,2,0,1,1,2,1,-1] |
| Symmetry type of based matrix | c |
| u-polynomial | 2t^3-2t^2-2t |
| Normalized Jones-Krushkal polynomial | 3z^2+20z+29 |
| Enhanced Jones-Krushkal polynomial | 3w^3z^2+20w^2z+29w |
| Inner characteristic polynomial | t^6+64t^4+30t^2+1 |
| Outer characteristic polynomial | t^7+92t^5+94t^3+5t |
| Flat arrow polynomial | 8*K1**3 - 4*K1**2 - 4*K1*K2 - 4*K1 + 2*K2 + 3 |
| 2-strand cable arrow polynomial | -64*K1**6 + 672*K1**4*K2 - 2304*K1**4 + 288*K1**3*K2*K3 + 32*K1**3*K3*K4 - 320*K1**3*K3 - 192*K1**2*K2**4 + 672*K1**2*K2**3 + 224*K1**2*K2**2*K4 - 4288*K1**2*K2**2 - 544*K1**2*K2*K4 + 6784*K1**2*K2 - 352*K1**2*K3**2 - 112*K1**2*K4**2 - 3884*K1**2 + 288*K1*K2**3*K3 + 64*K1*K2**2*K3*K4 - 960*K1*K2**2*K3 - 128*K1*K2**2*K5 - 32*K1*K2*K3*K4 + 4944*K1*K2*K3 - 32*K1*K2*K4*K5 + 680*K1*K3*K4 + 56*K1*K4*K5 - 64*K2**6 + 64*K2**4*K4 - 864*K2**4 - 352*K2**2*K3**2 - 48*K2**2*K4**2 + 880*K2**2*K4 - 2848*K2**2 + 160*K2*K3*K5 + 16*K2*K4*K6 - 1292*K3**2 - 232*K4**2 - 8*K5**2 + 3094 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{2, 6}, {3, 5}, {1, 4}], [{2, 6}, {5}, {1, 4}, {3}]] |
| If K is slice | False |