| Min(phi) over symmetries of the knot is: [-2,-2,0,1,1,2,-1,1,1,3,3,0,0,2,1,1,0,1,-1,-1,1] |
| Flat knots (up to 7 crossings) with same phi are :['6.1470'] |
| Arrow polynomial of the knot is: -14*K1**2 + 7*K2 + 8 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.1470', '6.1607'] |
| Outer characteristic polynomial of the knot is: t^7+45t^5+61t^3+7t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1470'] |
| 2-strand cable arrow polynomial of the knot is: -256*K1**6 - 128*K1**4*K2**2 + 2368*K1**4*K2 - 6112*K1**4 + 288*K1**3*K2*K3 - 1632*K1**3*K3 + 384*K1**2*K2**3 - 6288*K1**2*K2**2 - 288*K1**2*K2*K4 + 13264*K1**2*K2 - 576*K1**2*K3**2 - 6772*K1**2 - 1024*K1*K2**2*K3 + 8096*K1*K2*K3 + 1016*K1*K3*K4 - 536*K2**4 + 952*K2**2*K4 - 5760*K2**2 - 2340*K3**2 - 454*K4**2 + 5796 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1470'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.4770', 'vk6.4796', 'vk6.5105', 'vk6.5131', 'vk6.6336', 'vk6.6763', 'vk6.6793', 'vk6.8297', 'vk6.8315', 'vk6.8748', 'vk6.9667', 'vk6.9689', 'vk6.9976', 'vk6.9998', 'vk6.21008', 'vk6.21027', 'vk6.22430', 'vk6.22451', 'vk6.28460', 'vk6.40228', 'vk6.40255', 'vk6.42157', 'vk6.46726', 'vk6.46753', 'vk6.48809', 'vk6.49025', 'vk6.49035', 'vk6.49841', 'vk6.49855', 'vk6.51507', 'vk6.58969', 'vk6.69801'] |
| 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 | O1O2O3U1O4U5O6U4U6U3O5U2 |
| R3 orbit | {'O1O2O3U1O4U5O6U4U6U3O5U2'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U2O4U1U5U6O5U4O6U3 |
| Gauss code of K* | O1O2O3U4O5U6U5U3O6U1O4U2 |
| Gauss code of -K* | O1O2O3U2O4U3O5U1U6U5O6U4 |
| 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 0 -2 1],[ 2 0 2 1 0 1 0],[-1 -2 0 1 0 -3 1],[-2 -1 -1 0 -1 -3 1],[ 0 0 0 1 0 -1 1],[ 2 -1 3 3 1 0 1],[-1 0 -1 -1 -1 -1 0]] |
| Primitive based matrix | [[ 0 2 1 1 0 -2 -2],[-2 0 1 -1 -1 -1 -3],[-1 -1 0 -1 -1 0 -1],[-1 1 1 0 0 -2 -3],[ 0 1 1 0 0 0 -1],[ 2 1 0 2 0 0 1],[ 2 3 1 3 1 -1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,-1,0,2,2,-1,1,1,1,3,1,1,0,1,0,2,3,0,1,-1] |
| Phi over symmetry | [-2,-2,0,1,1,2,-1,1,1,3,3,0,0,2,1,1,0,1,-1,-1,1] |
| Phi of -K | [-2,-2,0,1,1,2,-1,2,1,3,3,1,0,2,1,1,0,1,-1,0,2] |
| Phi of K* | [-2,-1,-1,0,2,2,0,2,1,1,3,1,1,0,1,0,2,3,1,2,-1] |
| Phi of -K* | [-2,-2,0,1,1,2,-1,1,1,3,3,0,0,2,1,1,0,1,-1,-1,1] |
| 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+31t^4+34t^2 |
| Outer characteristic polynomial | t^7+45t^5+61t^3+7t |
| Flat arrow polynomial | -14*K1**2 + 7*K2 + 8 |
| 2-strand cable arrow polynomial | -256*K1**6 - 128*K1**4*K2**2 + 2368*K1**4*K2 - 6112*K1**4 + 288*K1**3*K2*K3 - 1632*K1**3*K3 + 384*K1**2*K2**3 - 6288*K1**2*K2**2 - 288*K1**2*K2*K4 + 13264*K1**2*K2 - 576*K1**2*K3**2 - 6772*K1**2 - 1024*K1*K2**2*K3 + 8096*K1*K2*K3 + 1016*K1*K3*K4 - 536*K2**4 + 952*K2**2*K4 - 5760*K2**2 - 2340*K3**2 - 454*K4**2 + 5796 |
| Genus of based matrix | 2 |
| Fillings of based matrix | [[{1, 6}, {2, 5}, {3, 4}], [{1, 6}, {2, 5}, {4}, {3}], [{1, 6}, {3, 5}, {2, 4}], [{1, 6}, {3, 5}, {4}, {2}], [{1, 6}, {4, 5}, {2, 3}], [{1, 6}, {4, 5}, {3}, {2}], [{1, 6}, {5}, {2, 4}, {3}], [{1, 6}, {5}, {3, 4}, {2}], [{1, 6}, {5}, {4}, {2, 3}], [{2, 6}, {1, 5}, {3, 4}], [{2, 6}, {1, 5}, {4}, {3}], [{2, 6}, {3, 5}, {1, 4}], [{2, 6}, {3, 5}, {4}, {1}], [{2, 6}, {4, 5}, {1, 3}], [{2, 6}, {4, 5}, {3}, {1}], [{2, 6}, {5}, {1, 4}, {3}], [{2, 6}, {5}, {3, 4}, {1}], [{2, 6}, {5}, {4}, {1, 3}], [{3, 6}, {1, 5}, {2, 4}], [{3, 6}, {1, 5}, {4}, {2}], [{3, 6}, {2, 5}, {1, 4}], [{3, 6}, {2, 5}, {4}, {1}], [{3, 6}, {4, 5}, {1, 2}], [{3, 6}, {4, 5}, {2}, {1}], [{3, 6}, {5}, {1, 4}, {2}], [{3, 6}, {5}, {2, 4}, {1}], [{3, 6}, {5}, {4}, {1, 2}], [{4, 6}, {1, 5}, {2, 3}], [{4, 6}, {1, 5}, {3}, {2}], [{4, 6}, {2, 5}, {1, 3}], [{4, 6}, {2, 5}, {3}, {1}], [{4, 6}, {3, 5}, {1, 2}], [{4, 6}, {3, 5}, {2}, {1}], [{4, 6}, {5}, {1, 3}, {2}], [{4, 6}, {5}, {2, 3}, {1}], [{4, 6}, {5}, {3}, {1, 2}], [{5, 6}, {1, 4}, {2, 3}], [{5, 6}, {1, 4}, {3}, {2}], [{5, 6}, {2, 4}, {1, 3}], [{5, 6}, {2, 4}, {3}, {1}], [{5, 6}, {3, 4}, {1, 2}], [{5, 6}, {3, 4}, {2}, {1}], [{5, 6}, {4}, {1, 3}, {2}], [{5, 6}, {4}, {2, 3}, {1}], [{5, 6}, {4}, {3}, {1, 2}], [{6}, {1, 5}, {2, 4}, {3}], [{6}, {1, 5}, {3, 4}, {2}], [{6}, {1, 5}, {4}, {2, 3}], [{6}, {2, 5}, {1, 4}, {3}], [{6}, {2, 5}, {3, 4}, {1}], [{6}, {2, 5}, {4}, {1, 3}], [{6}, {3, 5}, {1, 4}, {2}], [{6}, {3, 5}, {2, 4}, {1}], [{6}, {3, 5}, {4}, {1, 2}], [{6}, {4, 5}, {1, 3}, {2}], [{6}, {4, 5}, {2, 3}, {1}], [{6}, {4, 5}, {3}, {1, 2}], [{6}, {5}, {1, 4}, {2, 3}], [{6}, {5}, {2, 4}, {1, 3}], [{6}, {5}, {2, 4}, {3}, {1}], [{6}, {5}, {3, 4}, {1, 2}], [{6}, {5}, {4}, {1, 3}, {2}]] |
| If K is slice | False |