| Min(phi) over symmetries of the knot is: [-3,-2,0,1,1,3,0,1,1,2,3,0,2,3,3,0,0,0,0,1,2] |
| Flat knots (up to 7 crossings) with same phi are :['6.617'] |
| Arrow polynomial of the knot is: -2*K1**2 - 4*K1*K2 + 2*K1 + K2 + 2*K3 + 2 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.120', '6.213', '6.216', '6.320', '6.322', '6.615', '6.617', '6.891', '6.951', '6.955', '6.1001', '6.1012', '6.1022', '6.1043', '6.1047', '6.1063', '6.1074', '6.1249', '6.1544', '6.1546', '6.1555', '6.1573', '6.1574', '6.1585', '6.1756', '6.1757', '6.1762', '6.1802', '6.1803', '6.1824', '6.1881', '6.1935'] |
| Outer characteristic polynomial of the knot is: t^7+72t^5+227t^3+7t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.617'] |
| 2-strand cable arrow polynomial of the knot is: -528*K1**2*K2**2 - 224*K1**2*K2*K4 + 1448*K1**2*K2 - 176*K1**2*K3**2 - 2516*K1**2 + 96*K1*K2**2*K3*K4 - 864*K1*K2**2*K3 + 32*K1*K2*K3**3 + 3136*K1*K2*K3 - 64*K1*K2*K4*K5 + 1640*K1*K3*K4 + 8*K1*K4*K5 + 8*K1*K5*K6 - 8*K2**4 - 128*K2**2*K3**2 - 112*K2**2*K4**2 + 1112*K2**2*K4 - 2496*K2**2 - 160*K2*K3**2*K4 + 64*K2*K3*K5 + 152*K2*K4*K6 - 16*K3**4 + 32*K3**2*K6 - 1780*K3**2 - 1054*K4**2 - 8*K5**2 - 24*K6**2 + 2428 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.617'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.73321', 'vk6.73463', 'vk6.74025', 'vk6.74579', 'vk6.75213', 'vk6.75470', 'vk6.76057', 'vk6.76776', 'vk6.78206', 'vk6.78436', 'vk6.79007', 'vk6.79579', 'vk6.80021', 'vk6.80173', 'vk6.80544', 'vk6.80999', 'vk6.81887', 'vk6.82351', 'vk6.82375', 'vk6.82605', 'vk6.83631', 'vk6.83670', 'vk6.84304', 'vk6.84356', 'vk6.84473', 'vk6.84579', 'vk6.84633', 'vk6.85235', 'vk6.85600', 'vk6.86767', 'vk6.88700', 'vk6.88987'] |
| 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 | O1O2O3O4U5O6U1O5U3U2U6U4 |
| R3 orbit | {'O1O2O3O4U5O6U1O5U3U2U6U4'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U1U5U3U2O6U4O5U6 |
| Gauss code of K* | O1O2O3O4U5U2U1U4O6U3O5U6 |
| Gauss code of -K* | O1O2O3O4U5O6U2O5U1U4U3U6 |
| 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 -1 3 0 2],[ 3 0 1 0 3 3 2],[ 1 -1 0 0 3 1 1],[ 1 0 0 0 2 1 0],[-3 -3 -3 -2 0 -2 -1],[ 0 -3 -1 -1 2 0 2],[-2 -2 -1 0 1 -2 0]] |
| Primitive based matrix | [[ 0 3 2 0 -1 -1 -3],[-3 0 -1 -2 -2 -3 -3],[-2 1 0 -2 0 -1 -2],[ 0 2 2 0 -1 -1 -3],[ 1 2 0 1 0 0 0],[ 1 3 1 1 0 0 -1],[ 3 3 2 3 0 1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-3,-2,0,1,1,3,1,2,2,3,3,2,0,1,2,1,1,3,0,0,1] |
| Phi over symmetry | [-3,-2,0,1,1,3,0,1,1,2,3,0,2,3,3,0,0,0,0,1,2] |
| Phi of -K | [-3,-1,-1,0,2,3,1,2,0,3,3,0,0,2,1,0,3,2,0,1,0] |
| Phi of K* | [-3,-2,0,1,1,3,0,1,1,2,3,0,2,3,3,0,0,0,0,1,2] |
| Phi of -K* | [-3,-1,-1,0,2,3,0,1,3,2,3,0,1,0,2,1,1,3,2,2,1] |
| Symmetry type of based matrix | c |
| u-polynomial | -t^2+2t |
| Normalized Jones-Krushkal polynomial | 4z^2+17z+19 |
| Enhanced Jones-Krushkal polynomial | -2w^4z^2+6w^3z^2-6w^3z+23w^2z+19w |
| Inner characteristic polynomial | t^6+48t^4+136t^2 |
| Outer characteristic polynomial | t^7+72t^5+227t^3+7t |
| Flat arrow polynomial | -2*K1**2 - 4*K1*K2 + 2*K1 + K2 + 2*K3 + 2 |
| 2-strand cable arrow polynomial | -528*K1**2*K2**2 - 224*K1**2*K2*K4 + 1448*K1**2*K2 - 176*K1**2*K3**2 - 2516*K1**2 + 96*K1*K2**2*K3*K4 - 864*K1*K2**2*K3 + 32*K1*K2*K3**3 + 3136*K1*K2*K3 - 64*K1*K2*K4*K5 + 1640*K1*K3*K4 + 8*K1*K4*K5 + 8*K1*K5*K6 - 8*K2**4 - 128*K2**2*K3**2 - 112*K2**2*K4**2 + 1112*K2**2*K4 - 2496*K2**2 - 160*K2*K3**2*K4 + 64*K2*K3*K5 + 152*K2*K4*K6 - 16*K3**4 + 32*K3**2*K6 - 1780*K3**2 - 1054*K4**2 - 8*K5**2 - 24*K6**2 + 2428 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{4, 6}, {2, 5}, {1, 3}]] |
| If K is slice | False |