| Min(phi) over symmetries of the knot is: [-3,-1,-1,1,2,2,0,1,2,2,3,1,1,1,1,1,1,1,1,0,-2] |
| Flat knots (up to 7 crossings) with same phi are :['6.207'] |
| Arrow polynomial of the knot is: -4*K1**2 - 2*K1*K2 + K1 + 2*K2 + K3 + 3 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.136', '6.207', '6.342', '6.370', '6.376', '6.442', '6.456', '6.539', '6.631', '6.636', '6.674', '6.679', '6.705', '6.740', '6.760', '6.794', '6.795', '6.1369'] |
| Outer characteristic polynomial of the knot is: t^7+66t^5+63t^3+8t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.207'] |
| 2-strand cable arrow polynomial of the knot is: -704*K1**4*K2**2 + 1344*K1**4*K2 - 1392*K1**4 + 96*K1**3*K2*K3 - 160*K1**3*K3 + 1472*K1**2*K2**3 - 7056*K1**2*K2**2 - 352*K1**2*K2*K4 + 6888*K1**2*K2 - 16*K1**2*K3**2 - 4736*K1**2 + 1056*K1*K2**3*K3 + 416*K1*K2**2*K3*K4 - 1408*K1*K2**2*K3 - 96*K1*K2**2*K5 - 544*K1*K2*K3*K4 - 32*K1*K2*K3*K6 + 7336*K1*K2*K3 + 784*K1*K3*K4 + 32*K1*K4*K5 - 2032*K2**4 - 1712*K2**2*K3**2 - 296*K2**2*K4**2 + 2144*K2**2*K4 - 3254*K2**2 + 992*K2*K3*K5 + 64*K2*K4*K6 - 2108*K3**2 - 632*K4**2 - 100*K5**2 - 2*K6**2 + 4006 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.207'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.4190', 'vk6.4269', 'vk6.5436', 'vk6.5552', 'vk6.7547', 'vk6.7628', 'vk6.9055', 'vk6.9134', 'vk6.18250', 'vk6.18585', 'vk6.24726', 'vk6.25139', 'vk6.36852', 'vk6.37315', 'vk6.44081', 'vk6.44420', 'vk6.48502', 'vk6.48581', 'vk6.49186', 'vk6.49296', 'vk6.50283', 'vk6.50353', 'vk6.51052', 'vk6.51083', 'vk6.56045', 'vk6.56319', 'vk6.60598', 'vk6.60941', 'vk6.65711', 'vk6.66005', 'vk6.68752', 'vk6.68960'] |
| 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 | O1O2O3O4O5U2O6U4U5U6U1U3 |
| R3 orbit | {'O1O2O3O4O5U2O6U4U5U6U1U3'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4O5U3U5U6U1U2O6U4 |
| Gauss code of K* | O1O2O3O4O5U4U6U5U1U2O6U3 |
| Gauss code of -K* | O1O2O3O4O5U3O6U4U5U1U6U2 |
| 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 -1 -3 2 -1 1 2],[ 1 0 -2 2 -1 1 2],[ 3 2 0 3 1 2 2],[-2 -2 -3 0 -2 0 2],[ 1 1 -1 2 0 1 2],[-1 -1 -2 0 -1 0 1],[-2 -2 -2 -2 -2 -1 0]] |
| Primitive based matrix | [[ 0 2 2 1 -1 -1 -3],[-2 0 2 0 -2 -2 -3],[-2 -2 0 -1 -2 -2 -2],[-1 0 1 0 -1 -1 -2],[ 1 2 2 1 0 1 -1],[ 1 2 2 1 -1 0 -2],[ 3 3 2 2 1 2 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-2,-1,1,1,3,-2,0,2,2,3,1,2,2,2,1,1,2,-1,1,2] |
| Phi over symmetry | [-3,-1,-1,1,2,2,0,1,2,2,3,1,1,1,1,1,1,1,1,0,-2] |
| Phi of -K | [-3,-1,-1,1,2,2,0,1,2,2,3,1,1,1,1,1,1,1,1,0,-2] |
| Phi of K* | [-2,-2,-1,1,1,3,-2,0,1,1,3,1,1,1,2,1,1,2,-1,0,1] |
| Phi of -K* | [-3,-1,-1,1,2,2,1,2,2,2,3,1,1,2,2,1,2,2,1,0,-2] |
| Symmetry type of based matrix | c |
| u-polynomial | t^3-2t^2+t |
| Normalized Jones-Krushkal polynomial | 8z^2+29z+27 |
| Enhanced Jones-Krushkal polynomial | 8w^3z^2+29w^2z+27w |
| Inner characteristic polynomial | t^6+46t^4+15t^2+1 |
| Outer characteristic polynomial | t^7+66t^5+63t^3+8t |
| Flat arrow polynomial | -4*K1**2 - 2*K1*K2 + K1 + 2*K2 + K3 + 3 |
| 2-strand cable arrow polynomial | -704*K1**4*K2**2 + 1344*K1**4*K2 - 1392*K1**4 + 96*K1**3*K2*K3 - 160*K1**3*K3 + 1472*K1**2*K2**3 - 7056*K1**2*K2**2 - 352*K1**2*K2*K4 + 6888*K1**2*K2 - 16*K1**2*K3**2 - 4736*K1**2 + 1056*K1*K2**3*K3 + 416*K1*K2**2*K3*K4 - 1408*K1*K2**2*K3 - 96*K1*K2**2*K5 - 544*K1*K2*K3*K4 - 32*K1*K2*K3*K6 + 7336*K1*K2*K3 + 784*K1*K3*K4 + 32*K1*K4*K5 - 2032*K2**4 - 1712*K2**2*K3**2 - 296*K2**2*K4**2 + 2144*K2**2*K4 - 3254*K2**2 + 992*K2*K3*K5 + 64*K2*K4*K6 - 2108*K3**2 - 632*K4**2 - 100*K5**2 - 2*K6**2 + 4006 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{3, 6}, {2, 5}, {1, 4}]] |
| If K is slice | False |