| Min(phi) over symmetries of the knot is: [-2,-1,0,1,1,1,0,1,1,1,2,0,0,1,1,1,1,1,0,-1,-1] |
| Flat knots (up to 7 crossings) with same phi are :['6.1038'] |
| 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+28t^5+24t^3+4t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1038'] |
| 2-strand cable arrow polynomial of the knot is: -128*K1**6 + 704*K1**4*K2 - 2144*K1**4 + 96*K1**3*K2*K3 - 928*K1**3*K3 - 944*K1**2*K2**2 - 384*K1**2*K2*K4 + 4088*K1**2*K2 - 256*K1**2*K3**2 - 64*K1**2*K4**2 - 2352*K1**2 - 160*K1*K2**2*K3 - 32*K1*K2**2*K5 - 128*K1*K2*K3*K4 + 2632*K1*K2*K3 + 848*K1*K3*K4 + 144*K1*K4*K5 - 24*K2**4 - 48*K2**2*K3**2 - 48*K2**2*K4**2 + 384*K2**2*K4 - 1972*K2**2 + 128*K2*K3*K5 + 32*K2*K4*K6 - 1004*K3**2 - 414*K4**2 - 68*K5**2 - 4*K6**2 + 2044 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1038'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.4466', 'vk6.4561', 'vk6.5848', 'vk6.5975', 'vk6.6406', 'vk6.6837', 'vk6.8024', 'vk6.8363', 'vk6.9335', 'vk6.9454', 'vk6.11627', 'vk6.11978', 'vk6.12973', 'vk6.13423', 'vk6.13518', 'vk6.13711', 'vk6.14066', 'vk6.15043', 'vk6.15163', 'vk6.17781', 'vk6.17812', 'vk6.18847', 'vk6.19426', 'vk6.19721', 'vk6.24328', 'vk6.25446', 'vk6.25477', 'vk6.26600', 'vk6.33277', 'vk6.33336', 'vk6.37566', 'vk6.39274', 'vk6.39751', 'vk6.41454', 'vk6.44875', 'vk6.46315', 'vk6.47892', 'vk6.48653', 'vk6.49895', 'vk6.53238'] |
| 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 | O1O2O3O4U5U2O5U3O6U4U1U6 |
| R3 orbit | {'O1O2O3O4U3U5U2O5O6U4U1U6', 'O1O2O3O4U5U2O5U3O6U4U1U6'} |
| R3 orbit length | 2 |
| Gauss code of -K | O1O2O3O4U5U4U1O5U2O6U3U6 |
| Gauss code of K* | O1O2O3U2U4U5U1O6O4U6O5U3 |
| Gauss code of -K* | O1O2O3U1O4U5O6O5U3U4U6U2 |
| 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 -1 0 1 -1 2],[ 1 0 -1 0 2 0 2],[ 1 1 0 0 1 1 1],[ 0 0 0 0 1 0 1],[-1 -2 -1 -1 0 -1 1],[ 1 0 -1 0 1 0 2],[-2 -2 -1 -1 -1 -2 0]] |
| Primitive based matrix | [[ 0 2 1 0 -1 -1 -1],[-2 0 -1 -1 -1 -2 -2],[-1 1 0 -1 -1 -1 -2],[ 0 1 1 0 0 0 0],[ 1 1 1 0 0 1 1],[ 1 2 1 0 -1 0 0],[ 1 2 2 0 -1 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,0,1,1,1,1,1,1,2,2,1,1,1,2,0,0,0,-1,-1,0] |
| Phi over symmetry | [-2,-1,0,1,1,1,0,1,1,1,2,0,0,1,1,1,1,1,0,-1,-1] |
| Phi of -K | [-1,-1,-1,0,1,2,-1,-1,1,1,2,0,1,0,1,1,1,1,0,1,0] |
| Phi of K* | [-2,-1,0,1,1,1,0,1,1,1,2,0,0,1,1,1,1,1,0,-1,-1] |
| Phi of -K* | [-1,-1,-1,0,1,2,-1,0,0,1,2,1,0,1,1,0,2,2,1,1,1] |
| Symmetry type of based matrix | c |
| u-polynomial | -t^2+2t |
| Normalized Jones-Krushkal polynomial | 13z+27 |
| Enhanced Jones-Krushkal polynomial | 13w^2z+27w |
| Inner characteristic polynomial | t^6+20t^4+11t^2+1 |
| Outer characteristic polynomial | t^7+28t^5+24t^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 + 704*K1**4*K2 - 2144*K1**4 + 96*K1**3*K2*K3 - 928*K1**3*K3 - 944*K1**2*K2**2 - 384*K1**2*K2*K4 + 4088*K1**2*K2 - 256*K1**2*K3**2 - 64*K1**2*K4**2 - 2352*K1**2 - 160*K1*K2**2*K3 - 32*K1*K2**2*K5 - 128*K1*K2*K3*K4 + 2632*K1*K2*K3 + 848*K1*K3*K4 + 144*K1*K4*K5 - 24*K2**4 - 48*K2**2*K3**2 - 48*K2**2*K4**2 + 384*K2**2*K4 - 1972*K2**2 + 128*K2*K3*K5 + 32*K2*K4*K6 - 1004*K3**2 - 414*K4**2 - 68*K5**2 - 4*K6**2 + 2044 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {3, 5}, {2, 4}], [{1, 6}, {3, 5}, {4}, {2}], [{3, 6}, {1, 5}, {2, 4}], [{5, 6}, {2, 4}, {1, 3}]] |
| If K is slice | False |