| Min(phi) over symmetries of the knot is: [-3,-2,0,1,2,2,0,2,3,2,3,1,2,2,2,1,2,1,2,1,-1] |
| Flat knots (up to 7 crossings) with same phi are :['6.338'] |
| Arrow polynomial of the knot is: 4*K1**3 - 2*K1**2 - 2*K1*K2 - 2*K1 + K2 + 2 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['4.2', '6.303', '6.338', '6.381', '6.432', '6.468', '6.558', '6.583', '6.597', '6.607', '6.634', '6.637', '6.643', '6.654', '6.667', '6.701', '6.709', '6.712', '6.718', '6.728', '6.767', '6.801', '6.825', '6.827', '6.974', '6.994', '6.1042', '6.1061', '6.1069', '6.1181', '6.1271', '6.1286', '6.1287', '6.1289', '6.1297', '6.1337', '6.1355'] |
| Outer characteristic polynomial of the knot is: t^7+73t^5+61t^3+4t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.338'] |
| 2-strand cable arrow polynomial of the knot is: -256*K1**4*K2**2 + 448*K1**4*K2 - 416*K1**4 + 128*K1**3*K2*K3 - 64*K1**3*K3 - 192*K1**2*K2**4 + 768*K1**2*K2**3 - 3200*K1**2*K2**2 - 192*K1**2*K2*K4 + 2696*K1**2*K2 - 1436*K1**2 + 192*K1*K2**3*K3 - 224*K1*K2**2*K3 - 32*K1*K2**2*K5 + 2072*K1*K2*K3 + 40*K1*K3*K4 - 32*K2**6 + 32*K2**4*K4 - 584*K2**4 - 48*K2**2*K3**2 - 8*K2**2*K4**2 + 384*K2**2*K4 - 728*K2**2 + 16*K2*K3*K5 - 300*K3**2 - 50*K4**2 + 984 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.338'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.16917', 'vk6.17159', 'vk6.17501', 'vk6.17509', 'vk6.17556', 'vk6.17564', 'vk6.21894', 'vk6.24025', 'vk6.24037', 'vk6.24104', 'vk6.27950', 'vk6.29429', 'vk6.35331', 'vk6.35763', 'vk6.36281', 'vk6.36291', 'vk6.36356', 'vk6.39360', 'vk6.41537', 'vk6.43434', 'vk6.43442', 'vk6.43469', 'vk6.45923', 'vk6.47612', 'vk6.55068', 'vk6.55317', 'vk6.55615', 'vk6.55623', 'vk6.55650', 'vk6.58545', 'vk6.60125', 'vk6.60137', 'vk6.60167', 'vk6.63031', 'vk6.64905', 'vk6.65118', 'vk6.65318', 'vk6.65356', 'vk6.68490', 'vk6.68517'] |
| 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 | O1O2O3O4O5U3U1O6U4U5U6U2 |
| R3 orbit | {'O1O2O3O4O5U3U1O6U4U5U6U2', 'O1O2O3O4U5U1O6U3U4U6O5U2'} |
| R3 orbit length | 2 |
| Gauss code of -K | O1O2O3O4O5U4U6U1U2O6U5U3 |
| Gauss code of K* | O1O2O3O4U5U4U6U1U2O6O5U3 |
| Gauss code of -K* | O1O2O3O4U2O5O6U3U4U6U1U5 |
| 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 -3 1 -2 0 2 2],[ 3 0 3 0 2 3 2],[-1 -3 0 -2 -1 1 2],[ 2 0 2 0 1 2 2],[ 0 -2 1 -1 0 1 2],[-2 -3 -1 -2 -1 0 1],[-2 -2 -2 -2 -2 -1 0]] |
| Primitive based matrix | [[ 0 2 2 1 0 -2 -3],[-2 0 1 -1 -1 -2 -3],[-2 -1 0 -2 -2 -2 -2],[-1 1 2 0 -1 -2 -3],[ 0 1 2 1 0 -1 -2],[ 2 2 2 2 1 0 0],[ 3 3 2 3 2 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-2,-1,0,2,3,-1,1,1,2,3,2,2,2,2,1,2,3,1,2,0] |
| Phi over symmetry | [-3,-2,0,1,2,2,0,2,3,2,3,1,2,2,2,1,2,1,2,1,-1] |
| Phi of -K | [-3,-2,0,1,2,2,1,1,1,2,3,1,1,2,2,0,1,0,0,-1,-1] |
| Phi of K* | [-2,-2,-1,0,2,3,-1,-1,0,2,3,0,1,2,2,0,1,1,1,1,1] |
| Phi of -K* | [-3,-2,0,1,2,2,0,2,3,2,3,1,2,2,2,1,2,1,2,1,-1] |
| Symmetry type of based matrix | c |
| u-polynomial | t^3-t^2-t |
| Normalized Jones-Krushkal polynomial | 5z^2+18z+17 |
| Enhanced Jones-Krushkal polynomial | 5w^3z^2+18w^2z+17w |
| Inner characteristic polynomial | t^6+51t^4+26t^2+1 |
| Outer characteristic polynomial | t^7+73t^5+61t^3+4t |
| Flat arrow polynomial | 4*K1**3 - 2*K1**2 - 2*K1*K2 - 2*K1 + K2 + 2 |
| 2-strand cable arrow polynomial | -256*K1**4*K2**2 + 448*K1**4*K2 - 416*K1**4 + 128*K1**3*K2*K3 - 64*K1**3*K3 - 192*K1**2*K2**4 + 768*K1**2*K2**3 - 3200*K1**2*K2**2 - 192*K1**2*K2*K4 + 2696*K1**2*K2 - 1436*K1**2 + 192*K1*K2**3*K3 - 224*K1*K2**2*K3 - 32*K1*K2**2*K5 + 2072*K1*K2*K3 + 40*K1*K3*K4 - 32*K2**6 + 32*K2**4*K4 - 584*K2**4 - 48*K2**2*K3**2 - 8*K2**2*K4**2 + 384*K2**2*K4 - 728*K2**2 + 16*K2*K3*K5 - 300*K3**2 - 50*K4**2 + 984 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{2, 6}, {1, 5}, {3, 4}], [{4, 6}, {1, 5}, {2, 3}]] |
| If K is slice | False |