| Min(phi) over symmetries of the knot is: [-2,-2,0,1,1,2,-1,1,1,1,3,0,0,1,2,1,0,1,0,-1,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.1006'] |
| Arrow polynomial of the knot is: -6*K1**2 - 4*K1*K2 + 2*K1 + 3*K2 + 2*K3 + 4 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.239', '6.428', '6.470', '6.556', '6.700', '6.910', '6.962', '6.1006', '6.1013', '6.1038', '6.1207', '6.1224', '6.1225', '6.1269', '6.1270', '6.1308', '6.1319', '6.1320', '6.1323', '6.1485', '6.1551', '6.1579', '6.1581', '6.1660', '6.1672', '6.1679', '6.1711', '6.1719', '6.1732', '6.1745', '6.1748', '6.1827', '6.1836', '6.1838', '6.1850', '6.1866'] |
| Outer characteristic polynomial of the knot is: t^7+35t^5+48t^3+4t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1006'] |
| 2-strand cable arrow polynomial of the knot is: -128*K1**6 + 512*K1**4*K2 - 4464*K1**4 + 64*K1**3*K2*K3 - 160*K1**3*K3 - 2560*K1**2*K2**2 - 64*K1**2*K2*K4 + 7312*K1**2*K2 - 2128*K1**2*K3**2 - 32*K1**2*K3*K5 - 256*K1**2*K4**2 - 4340*K1**2 - 352*K1*K2**2*K3 - 128*K1*K2*K3*K4 + 6088*K1*K2*K3 + 3120*K1*K3*K4 + 344*K1*K4*K5 - 120*K2**4 - 176*K2**2*K3**2 - 48*K2**2*K4**2 + 544*K2**2*K4 - 4060*K2**2 + 264*K2*K3*K5 + 32*K2*K4*K6 - 2760*K3**2 - 1162*K4**2 - 156*K5**2 - 4*K6**2 + 4816 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1006'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.3651', 'vk6.3748', 'vk6.3941', 'vk6.4038', 'vk6.4472', 'vk6.4567', 'vk6.5858', 'vk6.5985', 'vk6.7136', 'vk6.7313', 'vk6.7406', 'vk6.7911', 'vk6.8030', 'vk6.9345', 'vk6.17921', 'vk6.18016', 'vk6.18764', 'vk6.24460', 'vk6.24887', 'vk6.25350', 'vk6.37511', 'vk6.43887', 'vk6.44242', 'vk6.44547', 'vk6.48275', 'vk6.48340', 'vk6.50058', 'vk6.50172', 'vk6.50572', 'vk6.50635', 'vk6.55880', 'vk6.60726'] |
| 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 | O1O2O3O4U2U4O5U1O6U5U6U3 |
| R3 orbit | {'O1O2O3O4U2U4O5U1O6U5U6U3'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U2U5U6O5U4O6U1U3 |
| Gauss code of K* | O1O2O3U4U5U3U6O5O6U1O4U2 |
| Gauss code of -K* | O1O2O3U2O4U3O5O6U5U1U6U4 |
| 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 0 1],[ 2 0 -1 3 1 1 1],[ 2 1 0 2 1 0 0],[-2 -3 -2 0 0 -1 1],[-1 -1 -1 0 0 0 0],[ 0 -1 0 1 0 0 1],[-1 -1 0 -1 0 -1 0]] |
| Primitive based matrix | [[ 0 2 1 1 0 -2 -2],[-2 0 1 0 -1 -2 -3],[-1 -1 0 0 -1 0 -1],[-1 0 0 0 0 -1 -1],[ 0 1 1 0 0 0 -1],[ 2 2 0 1 0 0 1],[ 2 3 1 1 1 -1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,-1,0,2,2,-1,0,1,2,3,0,1,0,1,0,1,1,0,1,-1] |
| Phi over symmetry | [-2,-2,0,1,1,2,-1,1,1,1,3,0,0,1,2,1,0,1,0,-1,0] |
| Phi of -K | [-2,-2,0,1,1,2,-1,2,2,3,2,1,2,2,1,1,0,1,0,1,2] |
| Phi of K* | [-2,-1,-1,0,2,2,1,2,1,1,2,0,1,2,2,0,2,3,1,2,-1] |
| Phi of -K* | [-2,-2,0,1,1,2,-1,1,1,1,3,0,0,1,2,1,0,1,0,-1,0] |
| Symmetry type of based matrix | c |
| u-polynomial | t^2-2t |
| Normalized Jones-Krushkal polynomial | 21z+43 |
| Enhanced Jones-Krushkal polynomial | 21w^2z+43w |
| Inner characteristic polynomial | t^6+21t^4+25t^2+1 |
| Outer characteristic polynomial | t^7+35t^5+48t^3+4t |
| Flat arrow polynomial | -6*K1**2 - 4*K1*K2 + 2*K1 + 3*K2 + 2*K3 + 4 |
| 2-strand cable arrow polynomial | -128*K1**6 + 512*K1**4*K2 - 4464*K1**4 + 64*K1**3*K2*K3 - 160*K1**3*K3 - 2560*K1**2*K2**2 - 64*K1**2*K2*K4 + 7312*K1**2*K2 - 2128*K1**2*K3**2 - 32*K1**2*K3*K5 - 256*K1**2*K4**2 - 4340*K1**2 - 352*K1*K2**2*K3 - 128*K1*K2*K3*K4 + 6088*K1*K2*K3 + 3120*K1*K3*K4 + 344*K1*K4*K5 - 120*K2**4 - 176*K2**2*K3**2 - 48*K2**2*K4**2 + 544*K2**2*K4 - 4060*K2**2 + 264*K2*K3*K5 + 32*K2*K4*K6 - 2760*K3**2 - 1162*K4**2 - 156*K5**2 - 4*K6**2 + 4816 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {3, 5}, {2, 4}], [{1, 6}, {3, 5}, {4}, {2}], [{2, 6}, {4, 5}, {1, 3}], [{4, 6}, {2, 5}, {1, 3}], [{4, 6}, {2, 5}, {3}, {1}], [{5, 6}, {2, 4}, {1, 3}]] |
| If K is slice | False |