| Min(phi) over symmetries of the knot is: [-2,-2,0,1,1,2,-1,0,1,2,2,1,1,2,2,1,0,1,-1,-1,1] |
| Flat knots (up to 7 crossings) with same phi are :['6.239'] |
| 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+39t^5+54t^3+5t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.239'] |
| 2-strand cable arrow polynomial of the knot is: -128*K1**6 + 800*K1**4*K2 - 2880*K1**4 + 128*K1**3*K2*K3 - 1184*K1**3*K3 - 1536*K1**2*K2**2 + 32*K1**2*K2*K3**2 - 448*K1**2*K2*K4 + 6544*K1**2*K2 - 672*K1**2*K3**2 - 80*K1**2*K4**2 - 4372*K1**2 - 352*K1*K2**2*K3 - 32*K1*K2**2*K5 - 320*K1*K2*K3*K4 + 4560*K1*K2*K3 + 1448*K1*K3*K4 + 248*K1*K4*K5 - 56*K2**4 - 112*K2**2*K3**2 - 48*K2**2*K4**2 + 664*K2**2*K4 - 3540*K2**2 + 272*K2*K3*K5 + 48*K2*K4*K6 - 1788*K3**2 - 694*K4**2 - 128*K5**2 - 12*K6**2 + 3636 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.239'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.3646', 'vk6.3741', 'vk6.3932', 'vk6.4027', 'vk6.4486', 'vk6.4581', 'vk6.5868', 'vk6.5995', 'vk6.7129', 'vk6.7304', 'vk6.7395', 'vk6.7917', 'vk6.8036', 'vk6.9347', 'vk6.17930', 'vk6.18027', 'vk6.18769', 'vk6.24465', 'vk6.24890', 'vk6.25351', 'vk6.37508', 'vk6.43892', 'vk6.44237', 'vk6.44540', 'vk6.48286', 'vk6.48349', 'vk6.50067', 'vk6.50177', 'vk6.50562', 'vk6.50625', 'vk6.55875', 'vk6.60729'] |
| 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 | O1O2O3O4O5U3O6U5U6U1U4U2 |
| R3 orbit | {'O1O2O3O4O5U3O6U5U6U1U4U2'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4O5U4U2U5U6U1O6U3 |
| Gauss code of K* | O1O2O3O4O5U3U5U6U4U1O6U2 |
| Gauss code of -K* | O1O2O3O4O5U4O6U5U2U6U1U3 |
| 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 -2 2 0 1],[ 2 0 2 -1 2 0 1],[-1 -2 0 -2 1 0 1],[ 2 1 2 0 2 1 1],[-2 -2 -1 -2 0 -1 1],[ 0 0 0 -1 1 0 1],[-1 -1 -1 -1 -1 -1 0]] |
| Primitive based matrix | [[ 0 2 1 1 0 -2 -2],[-2 0 1 -1 -1 -2 -2],[-1 -1 0 -1 -1 -1 -1],[-1 1 1 0 0 -2 -2],[ 0 1 1 0 0 0 -1],[ 2 2 1 2 0 0 -1],[ 2 2 1 2 1 1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,-1,0,2,2,-1,1,1,2,2,1,1,1,1,0,2,2,0,1,1] |
| Phi over symmetry | [-2,-2,0,1,1,2,-1,0,1,2,2,1,1,2,2,1,0,1,-1,-1,1] |
| Phi of -K | [-2,-2,0,1,1,2,-1,1,1,2,2,2,1,2,2,1,0,1,-1,0,2] |
| Phi of K* | [-2,-1,-1,0,2,2,0,2,1,2,2,1,1,1,1,0,2,2,1,2,1] |
| Phi of -K* | [-2,-2,0,1,1,2,-1,0,1,2,2,1,1,2,2,1,0,1,-1,-1,1] |
| Symmetry type of based matrix | c |
| u-polynomial | t^2-2t |
| Normalized Jones-Krushkal polynomial | 17z+35 |
| Enhanced Jones-Krushkal polynomial | 17w^2z+35w |
| Inner characteristic polynomial | t^6+25t^4+21t^2+1 |
| Outer characteristic polynomial | t^7+39t^5+54t^3+5t |
| Flat arrow polynomial | -6*K1**2 - 4*K1*K2 + 2*K1 + 3*K2 + 2*K3 + 4 |
| 2-strand cable arrow polynomial | -128*K1**6 + 800*K1**4*K2 - 2880*K1**4 + 128*K1**3*K2*K3 - 1184*K1**3*K3 - 1536*K1**2*K2**2 + 32*K1**2*K2*K3**2 - 448*K1**2*K2*K4 + 6544*K1**2*K2 - 672*K1**2*K3**2 - 80*K1**2*K4**2 - 4372*K1**2 - 352*K1*K2**2*K3 - 32*K1*K2**2*K5 - 320*K1*K2*K3*K4 + 4560*K1*K2*K3 + 1448*K1*K3*K4 + 248*K1*K4*K5 - 56*K2**4 - 112*K2**2*K3**2 - 48*K2**2*K4**2 + 664*K2**2*K4 - 3540*K2**2 + 272*K2*K3*K5 + 48*K2*K4*K6 - 1788*K3**2 - 694*K4**2 - 128*K5**2 - 12*K6**2 + 3636 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{3, 6}, {4, 5}, {1, 2}], [{3, 6}, {4, 5}, {2}, {1}]] |
| If K is slice | False |