| Min(phi) over symmetries of the knot is: [-1,-1,0,0,1,1,-1,0,1,1,2,0,0,1,2,-1,1,0,0,0,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.2015'] |
| 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+18t^5+42t^3+8t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.2015'] |
| 2-strand cable arrow polynomial of the knot is: -64*K1**6 - 64*K1**4*K2**2 + 672*K1**4*K2 - 3680*K1**4 + 256*K1**3*K2*K3 - 736*K1**3*K3 - 3744*K1**2*K2**2 - 128*K1**2*K2*K4 + 8240*K1**2*K2 - 288*K1**2*K3**2 - 3980*K1**2 + 4384*K1*K2*K3 + 312*K1*K3*K4 - 176*K2**4 + 152*K2**2*K4 - 3216*K2**2 - 1180*K3**2 - 112*K4**2 + 3350 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.2015'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.20017', 'vk6.20070', 'vk6.21287', 'vk6.21352', 'vk6.27064', 'vk6.27131', 'vk6.28767', 'vk6.28820', 'vk6.38465', 'vk6.38536', 'vk6.40652', 'vk6.40733', 'vk6.45345', 'vk6.45432', 'vk6.47112', 'vk6.47174', 'vk6.56832', 'vk6.56875', 'vk6.57964', 'vk6.58013', 'vk6.61346', 'vk6.61401', 'vk6.62520', 'vk6.62558', 'vk6.66552', 'vk6.66583', 'vk6.67339', 'vk6.67374', 'vk6.69194', 'vk6.69231', 'vk6.69943', 'vk6.69972'] |
| 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 | O1O2U3O4U2O5U1U6O3O6U5U4 |
| R3 orbit | {'O1O2U3O4U2O5U1U6O3O6U5U4'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2U3U4O5O6U5U2O4U1O3U6 |
| Gauss code of K* | O1O2U3U2O4O5U1U6O3U5O6U4 |
| Gauss code of -K* | O1O2U3O4U5O6U4U2O5O3U1U6 |
| 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 0 2 0 2],[ 0 0 0 0 0 -1 1],[ 1 0 0 0 1 1 1],[-1 -2 0 -1 0 0 -1],[ 0 0 1 -1 0 0 0],[-1 -2 -1 -1 1 0 0]] |
| Primitive based matrix | [[ 0 1 1 0 0 -1 -1],[-1 0 1 0 -1 -1 -2],[-1 -1 0 0 0 -1 -2],[ 0 0 0 0 1 -1 0],[ 0 1 0 -1 0 0 0],[ 1 1 1 1 0 0 0],[ 1 2 2 0 0 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-1,-1,0,0,1,1,-1,0,1,1,2,0,0,1,2,-1,1,0,0,0,0] |
| Phi over symmetry | [-1,-1,0,0,1,1,-1,0,1,1,2,0,0,1,2,-1,1,0,0,0,0] |
| Phi of -K | [-1,-1,0,0,1,1,0,0,1,1,1,1,1,0,0,-1,1,1,0,1,-1] |
| Phi of K* | [-1,-1,0,0,1,1,-1,1,1,0,1,0,1,0,1,-1,1,1,1,0,0] |
| Phi of -K* | [-1,-1,0,0,1,1,0,0,0,2,2,0,1,1,1,-1,0,1,0,0,-1] |
| Symmetry type of based matrix | c |
| u-polynomial | 0 |
| Normalized Jones-Krushkal polynomial | 17z+35 |
| Enhanced Jones-Krushkal polynomial | 17w^2z+35w |
| Inner characteristic polynomial | t^6+14t^4+28t^2+4 |
| Outer characteristic polynomial | t^7+18t^5+42t^3+8t |
| Flat arrow polynomial | -12*K1**2 + 6*K2 + 7 |
| 2-strand cable arrow polynomial | -64*K1**6 - 64*K1**4*K2**2 + 672*K1**4*K2 - 3680*K1**4 + 256*K1**3*K2*K3 - 736*K1**3*K3 - 3744*K1**2*K2**2 - 128*K1**2*K2*K4 + 8240*K1**2*K2 - 288*K1**2*K3**2 - 3980*K1**2 + 4384*K1*K2*K3 + 312*K1*K3*K4 - 176*K2**4 + 152*K2**2*K4 - 3216*K2**2 - 1180*K3**2 - 112*K4**2 + 3350 |
| Genus of based matrix | 0 |
| Fillings of based matrix | [[{3, 6}, {2, 5}, {1, 4}]] |
| If K is slice | True |