| Min(phi) over symmetries of the knot is: [-2,-1,0,1,1,1,0,2,1,1,1,0,0,1,1,1,1,2,1,1,-1] |
| Flat knots (up to 7 crossings) with same phi are :['6.1640'] |
| Arrow polynomial of the knot is: 8*K1**3 - 2*K1**2 - 4*K1*K2 - 4*K1 + K2 + 2 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.313', '6.623', '6.1031', '6.1201', '6.1327', '6.1378', '6.1640', '6.1697', '6.1797', '6.1833'] |
| Outer characteristic polynomial of the knot is: t^7+32t^5+76t^3+13t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1640'] |
| 2-strand cable arrow polynomial of the knot is: -448*K1**4*K2**2 + 800*K1**4*K2 - 768*K1**4 + 224*K1**3*K2*K3 - 160*K1**3*K3 - 1216*K1**2*K2**4 + 3072*K1**2*K2**3 + 32*K1**2*K2**2*K4 - 9680*K1**2*K2**2 - 160*K1**2*K2*K4 + 7656*K1**2*K2 - 4112*K1**2 + 1440*K1*K2**3*K3 - 1376*K1*K2**2*K3 - 32*K1*K2**2*K5 - 32*K1*K2*K3*K4 + 6136*K1*K2*K3 + 8*K1*K3*K4 - 64*K2**6 + 128*K2**4*K4 - 2152*K2**4 - 464*K2**2*K3**2 - 48*K2**2*K4**2 + 1120*K2**2*K4 - 1672*K2**2 + 48*K2*K3*K5 - 968*K3**2 - 62*K4**2 + 2748 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1640'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.4722', 'vk6.5039', 'vk6.6247', 'vk6.6697', 'vk6.8219', 'vk6.8657', 'vk6.9599', 'vk6.9926', 'vk6.20297', 'vk6.21630', 'vk6.27593', 'vk6.29145', 'vk6.39011', 'vk6.41259', 'vk6.45779', 'vk6.47456', 'vk6.48762', 'vk6.48965', 'vk6.49563', 'vk6.49775', 'vk6.50772', 'vk6.50978', 'vk6.51251', 'vk6.51456', 'vk6.57148', 'vk6.58332', 'vk6.61774', 'vk6.62893', 'vk6.66769', 'vk6.67645', 'vk6.69417', 'vk6.70139'] |
| 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 | O1O2O3U1O4U2U3U5O6O5U4U6 |
| R3 orbit | {'O1O2O3U1O4U2U3U5O6O5U4U6'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U4U5O6O4U6U1U2O5U3 |
| Gauss code of K* | O1O2O3U4U3O5O4U6U1U2O6U5 |
| Gauss code of -K* | O1O2O3U4O5U2U3U5O6O4U1U6 |
| 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 1 1 1 0],[ 2 0 1 2 2 2 0],[ 1 -1 0 1 2 1 1],[-1 -2 -1 0 1 -1 1],[-1 -2 -2 -1 0 -1 0],[-1 -2 -1 1 1 0 0],[ 0 0 -1 -1 0 0 0]] |
| Primitive based matrix | [[ 0 1 1 1 0 -1 -2],[-1 0 1 1 0 -1 -2],[-1 -1 0 1 1 -1 -2],[-1 -1 -1 0 0 -2 -2],[ 0 0 -1 0 0 -1 0],[ 1 1 1 2 1 0 -1],[ 2 2 2 2 0 1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-1,-1,-1,0,1,2,-1,-1,0,1,2,-1,-1,1,2,0,2,2,1,0,1] |
| Phi over symmetry | [-2,-1,0,1,1,1,0,2,1,1,1,0,0,1,1,1,1,2,1,1,-1] |
| Phi of -K | [-2,-1,0,1,1,1,0,2,1,1,1,0,0,1,1,1,1,2,1,1,-1] |
| Phi of K* | [-1,-1,-1,0,1,2,-1,-1,1,0,1,-1,2,1,1,1,1,1,0,2,0] |
| Phi of -K* | [-2,-1,0,1,1,1,1,0,2,2,2,1,1,1,2,-1,0,0,-1,1,1] |
| Symmetry type of based matrix | c |
| u-polynomial | t^2-2t |
| Normalized Jones-Krushkal polynomial | 6z^2+23z+23 |
| Enhanced Jones-Krushkal polynomial | 6w^3z^2-4w^3z+27w^2z+23w |
| Inner characteristic polynomial | t^6+24t^4+35t^2+1 |
| Outer characteristic polynomial | t^7+32t^5+76t^3+13t |
| Flat arrow polynomial | 8*K1**3 - 2*K1**2 - 4*K1*K2 - 4*K1 + K2 + 2 |
| 2-strand cable arrow polynomial | -448*K1**4*K2**2 + 800*K1**4*K2 - 768*K1**4 + 224*K1**3*K2*K3 - 160*K1**3*K3 - 1216*K1**2*K2**4 + 3072*K1**2*K2**3 + 32*K1**2*K2**2*K4 - 9680*K1**2*K2**2 - 160*K1**2*K2*K4 + 7656*K1**2*K2 - 4112*K1**2 + 1440*K1*K2**3*K3 - 1376*K1*K2**2*K3 - 32*K1*K2**2*K5 - 32*K1*K2*K3*K4 + 6136*K1*K2*K3 + 8*K1*K3*K4 - 64*K2**6 + 128*K2**4*K4 - 2152*K2**4 - 464*K2**2*K3**2 - 48*K2**2*K4**2 + 1120*K2**2*K4 - 1672*K2**2 + 48*K2*K3*K5 - 968*K3**2 - 62*K4**2 + 2748 |
| 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}], [{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}, {4, 5}, {3}, {2}, {1}], [{6}, {5}, {1, 4}, {2, 3}], [{6}, {5}, {2, 4}, {1, 3}], [{6}, {5}, {3, 4}, {1, 2}]] |
| If K is slice | False |