| Min(phi) over symmetries of the knot is: [-3,-2,0,1,2,2,0,2,2,1,3,2,1,2,3,1,0,1,1,0,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.704'] |
| Arrow polynomial of the knot is: 4*K1**3 - 6*K1**2 - 2*K1*K2 - 2*K1 + 3*K2 + 4 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.573', '6.628', '6.703', '6.704', '6.723', '6.796', '6.1083', '6.1099', '6.1315'] |
| Outer characteristic polynomial of the knot is: t^7+63t^5+197t^3 |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.704'] |
| 2-strand cable arrow polynomial of the knot is: 128*K1**4*K2**3 - 320*K1**4*K2**2 + 320*K1**4*K2 - 880*K1**4 + 96*K1**3*K2*K3 + 384*K1**2*K2**5 - 1920*K1**2*K2**4 + 2048*K1**2*K2**3 - 3648*K1**2*K2**2 + 3376*K1**2*K2 - 336*K1**2*K3**2 - 32*K1**2*K4**2 - 2264*K1**2 + 1024*K1*K2**3*K3 + 2432*K1*K2*K3 + 400*K1*K3*K4 + 88*K1*K4*K5 - 288*K2**6 + 64*K2**4*K4 - 840*K2**4 - 192*K2**2*K3**2 - 8*K2**2*K4**2 + 280*K2**2*K4 - 784*K2**2 + 32*K2*K3*K5 - 696*K3**2 - 218*K4**2 - 40*K5**2 + 1792 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.704'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.73700', 'vk6.73819', 'vk6.74199', 'vk6.74816', 'vk6.75615', 'vk6.75807', 'vk6.76370', 'vk6.76876', 'vk6.78594', 'vk6.78796', 'vk6.79234', 'vk6.79710', 'vk6.80240', 'vk6.80384', 'vk6.80718', 'vk6.81074', 'vk6.81612', 'vk6.81790', 'vk6.81928', 'vk6.82172', 'vk6.82301', 'vk6.82654', 'vk6.83190', 'vk6.84061', 'vk6.84220', 'vk6.84695', 'vk6.85014', 'vk6.86011', 'vk6.87751', 'vk6.88216', 'vk6.89401', 'vk6.89598'] |
| 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 | O1O2O3O4U5O6U2U3O5U1U6U4 |
| R3 orbit | {'O1O2O3O4U5O6U2U3O5U1U6U4'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U1U5U4O6U2U3O5U6 |
| Gauss code of K* | O1O2O3U1U4U5U3O6U2O4O5U6 |
| Gauss code of -K* | O1O2O3U4O5O6U2O4U1U5U6U3 |
| Diagrammatic symmetry type | c |
| Flat genus of the diagram | 2 |
| If K is checkerboard colorable | False |
| If K is almost classical | False |
| Based matrix from Gauss code | [[ 0 -2 -2 0 3 -1 2],[ 2 0 0 2 4 0 2],[ 2 0 0 1 2 1 1],[ 0 -2 -1 0 1 0 0],[-3 -4 -2 -1 0 -2 -1],[ 1 0 -1 0 2 0 2],[-2 -2 -1 0 1 -2 0]] |
| Primitive based matrix | [[ 0 3 2 0 -1 -2 -2],[-3 0 -1 -1 -2 -2 -4],[-2 1 0 0 -2 -1 -2],[ 0 1 0 0 0 -1 -2],[ 1 2 2 0 0 -1 0],[ 2 2 1 1 1 0 0],[ 2 4 2 2 0 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-3,-2,0,1,2,2,1,1,2,2,4,0,2,1,2,0,1,2,1,0,0] |
| Phi over symmetry | [-3,-2,0,1,2,2,0,2,2,1,3,2,1,2,3,1,0,1,1,0,0] |
| Phi of -K | [-2,-2,-1,0,2,3,0,0,1,3,3,1,0,2,1,1,1,2,2,2,0] |
| Phi of K* | [-3,-2,0,1,2,2,0,2,2,1,3,2,1,2,3,1,0,1,1,0,0] |
| Phi of -K* | [-2,-2,-1,0,2,3,0,0,2,2,4,1,1,1,2,0,2,2,0,1,1] |
| Symmetry type of based matrix | c |
| u-polynomial | -t^3+t^2+t |
| Normalized Jones-Krushkal polynomial | 9z+19 |
| Enhanced Jones-Krushkal polynomial | 4w^4z-8w^3z+13w^2z+19w |
| Inner characteristic polynomial | t^6+41t^4+90t^2 |
| Outer characteristic polynomial | t^7+63t^5+197t^3 |
| Flat arrow polynomial | 4*K1**3 - 6*K1**2 - 2*K1*K2 - 2*K1 + 3*K2 + 4 |
| 2-strand cable arrow polynomial | 128*K1**4*K2**3 - 320*K1**4*K2**2 + 320*K1**4*K2 - 880*K1**4 + 96*K1**3*K2*K3 + 384*K1**2*K2**5 - 1920*K1**2*K2**4 + 2048*K1**2*K2**3 - 3648*K1**2*K2**2 + 3376*K1**2*K2 - 336*K1**2*K3**2 - 32*K1**2*K4**2 - 2264*K1**2 + 1024*K1*K2**3*K3 + 2432*K1*K2*K3 + 400*K1*K3*K4 + 88*K1*K4*K5 - 288*K2**6 + 64*K2**4*K4 - 840*K2**4 - 192*K2**2*K3**2 - 8*K2**2*K4**2 + 280*K2**2*K4 - 784*K2**2 + 32*K2*K3*K5 - 696*K3**2 - 218*K4**2 - 40*K5**2 + 1792 |
| 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}], [{1, 6}, {5}, {4}, {3}, {2}], [{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}], [{2, 6}, {5}, {4}, {3}, {1}], [{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}], [{3, 6}, {5}, {4}, {2}, {1}], [{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}], [{4, 6}, {5}, {3}, {2}, {1}], [{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}], [{5, 6}, {4}, {3}, {2}, {1}], [{6}, {1, 5}, {2, 4}, {3}], [{6}, {1, 5}, {3, 4}, {2}], [{6}, {1, 5}, {4}, {2, 3}], [{6}, {1, 5}, {4}, {3}, {2}], [{6}, {2, 5}, {1, 4}, {3}], [{6}, {2, 5}, {3, 4}, {1}], [{6}, {2, 5}, {4}, {1, 3}], [{6}, {2, 5}, {4}, {3}, {1}], [{6}, {3, 5}, {1, 4}, {2}], [{6}, {3, 5}, {2, 4}, {1}], [{6}, {3, 5}, {4}, {1, 2}], [{6}, {3, 5}, {4}, {2}, {1}], [{6}, {4, 5}, {1, 3}, {2}], [{6}, {4, 5}, {2, 3}, {1}], [{6}, {4, 5}, {3}, {1, 2}], [{6}, {4, 5}, {3}, {2}, {1}], [{6}, {5}, {1, 4}, {2, 3}], [{6}, {5}, {1, 4}, {3}, {2}], [{6}, {5}, {2, 4}, {1, 3}], [{6}, {5}, {2, 4}, {3}, {1}], [{6}, {5}, {3, 4}, {1, 2}], [{6}, {5}, {3, 4}, {2}, {1}], [{6}, {5}, {4}, {1, 3}, {2}], [{6}, {5}, {4}, {2, 3}, {1}], [{6}, {5}, {4}, {3}, {1, 2}], [{6}, {5}, {4}, {3}, {2}, {1}]] |
| If K is slice | False |