| Min(phi) over symmetries of the knot is: [-1,-1,0,0,1,1,-1,0,0,1,2,0,1,1,1,0,0,1,1,1,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.1246', '6.1554'] |
| Arrow polynomial of the knot is: -12*K1**2 + 6*K2 + 7 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.612', '6.1246', '6.1402', '6.1410', '6.1411', '6.1468', '6.1617', '6.1666', '6.1667', '6.1815', '6.1904', '6.1994', '6.1995', '6.1996', '6.2001', '6.2014', '6.2015', '6.2016', '6.2017', '6.2020', '6.2022'] |
| Outer characteristic polynomial of the knot is: t^7+16t^5+16t^3+3t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1246'] |
| 2-strand cable arrow polynomial of the knot is: -448*K1**6 - 320*K1**4*K2**2 + 3904*K1**4*K2 - 7696*K1**4 + 384*K1**3*K2*K3 - 1088*K1**3*K3 + 2112*K1**2*K2**3 - 10560*K1**2*K2**2 - 352*K1**2*K2*K4 + 13184*K1**2*K2 - 176*K1**2*K3**2 - 3316*K1**2 - 1760*K1*K2**2*K3 + 6816*K1*K2*K3 + 320*K1*K3*K4 - 1600*K2**4 + 1328*K2**2*K4 - 3480*K2**2 - 1004*K3**2 - 144*K4**2 + 3894 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1246'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.11270', 'vk6.11348', 'vk6.12531', 'vk6.12642', 'vk6.17615', 'vk6.18930', 'vk6.19006', 'vk6.19354', 'vk6.19649', 'vk6.24075', 'vk6.24167', 'vk6.25526', 'vk6.25625', 'vk6.26126', 'vk6.26546', 'vk6.30952', 'vk6.31075', 'vk6.32128', 'vk6.32247', 'vk6.36412', 'vk6.37663', 'vk6.37710', 'vk6.43513', 'vk6.44779', 'vk6.52020', 'vk6.52111', 'vk6.52932', 'vk6.56493', 'vk6.56654', 'vk6.65380', 'vk6.66119', 'vk6.66153'] |
| 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 | O1O2O3O4U3U5U2O6O5U4U1U6 |
| R3 orbit | {'O1O2O3O4U3U5U2O6O5U4U1U6'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U5U4U1O6O5U3U6U2 |
| Gauss code of K* | O1O2O3U4U2O5O6O4U6U3U1U5 |
| Gauss code of -K* | O1O2O3U4U1O5O4O6U3U6U5U2 |
| 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 0 -1 1 0 1],[ 1 0 0 -1 2 0 1],[ 0 0 0 0 1 0 0],[ 1 1 0 0 1 1 1],[-1 -2 -1 -1 0 -1 0],[ 0 0 0 -1 1 0 1],[-1 -1 0 -1 0 -1 0]] |
| Primitive based matrix | [[ 0 1 1 0 0 -1 -1],[-1 0 0 0 -1 -1 -1],[-1 0 0 -1 -1 -1 -2],[ 0 0 1 0 0 0 0],[ 0 1 1 0 0 -1 0],[ 1 1 1 0 1 0 1],[ 1 1 2 0 0 -1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-1,-1,0,0,1,1,0,0,1,1,1,1,1,1,2,0,0,0,1,0,-1] |
| Phi over symmetry | [-1,-1,0,0,1,1,-1,0,0,1,2,0,1,1,1,0,0,1,1,1,0] |
| Phi of -K | [-1,-1,0,0,1,1,-1,0,1,1,1,1,1,0,1,0,0,0,0,1,0] |
| Phi of K* | [-1,-1,0,0,1,1,0,0,0,0,1,0,1,1,1,0,1,0,1,1,-1] |
| Phi of -K* | [-1,-1,0,0,1,1,-1,0,0,1,2,0,1,1,1,0,0,1,1,1,0] |
| Symmetry type of based matrix | c |
| u-polynomial | 0 |
| Normalized Jones-Krushkal polynomial | 3z^2+24z+37 |
| Enhanced Jones-Krushkal polynomial | 3w^3z^2+24w^2z+37w |
| Inner characteristic polynomial | t^6+12t^4+8t^2 |
| Outer characteristic polynomial | t^7+16t^5+16t^3+3t |
| Flat arrow polynomial | -12*K1**2 + 6*K2 + 7 |
| 2-strand cable arrow polynomial | -448*K1**6 - 320*K1**4*K2**2 + 3904*K1**4*K2 - 7696*K1**4 + 384*K1**3*K2*K3 - 1088*K1**3*K3 + 2112*K1**2*K2**3 - 10560*K1**2*K2**2 - 352*K1**2*K2*K4 + 13184*K1**2*K2 - 176*K1**2*K3**2 - 3316*K1**2 - 1760*K1*K2**2*K3 + 6816*K1*K2*K3 + 320*K1*K3*K4 - 1600*K2**4 + 1328*K2**2*K4 - 3480*K2**2 - 1004*K3**2 - 144*K4**2 + 3894 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {2, 5}, {3, 4}], [{3, 6}, {2, 5}, {1, 4}], [{3, 6}, {5}, {1, 4}, {2}]] |
| If K is slice | False |