| Min(phi) over symmetries of the knot is: [-2,-1,-1,1,1,2,0,1,0,2,1,1,1,1,1,1,2,3,-1,0,1] |
| Flat knots (up to 7 crossings) with same phi are :['6.1658'] |
| Arrow polynomial of the knot is: 4*K1**3 - 4*K1**2 - 4*K1*K2 - K1 + 2*K2 + K3 + 3 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.209', '6.231', '6.391', '6.419', '6.600', '6.661', '6.744', '6.812', '6.826', '6.1114', '6.1125', '6.1202', '6.1275', '6.1292', '6.1305', '6.1322', '6.1365', '6.1481', '6.1483', '6.1497', '6.1543', '6.1549', '6.1572', '6.1577', '6.1580', '6.1594', '6.1641', '6.1658', '6.1683', '6.1753', '6.1830', '6.1907', '6.1928'] |
| Outer characteristic polynomial of the knot is: t^7+38t^5+56t^3+11t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1658'] |
| 2-strand cable arrow polynomial of the knot is: 2528*K1**4*K2 - 5152*K1**4 + 864*K1**3*K2*K3 - 1120*K1**3*K3 - 128*K1**2*K2**4 + 1056*K1**2*K2**3 + 128*K1**2*K2**2*K4 - 8496*K1**2*K2**2 - 544*K1**2*K2*K4 + 10584*K1**2*K2 - 640*K1**2*K3**2 - 32*K1**2*K4**2 - 4280*K1**2 + 416*K1*K2**3*K3 - 1504*K1*K2**2*K3 - 192*K1*K2**2*K5 - 32*K1*K2*K3*K4 + 7552*K1*K2*K3 + 768*K1*K3*K4 + 32*K1*K4*K5 - 32*K2**6 + 64*K2**4*K4 - 880*K2**4 - 32*K2**3*K6 - 208*K2**2*K3**2 - 16*K2**2*K4**2 + 1016*K2**2*K4 - 3910*K2**2 + 104*K2*K3*K5 + 16*K2*K4*K6 - 1692*K3**2 - 248*K4**2 - 12*K5**2 - 2*K6**2 + 4022 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1658'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.4372', 'vk6.4403', 'vk6.5694', 'vk6.5725', 'vk6.7755', 'vk6.7786', 'vk6.9237', 'vk6.9268', 'vk6.10488', 'vk6.10562', 'vk6.10659', 'vk6.10711', 'vk6.10742', 'vk6.10844', 'vk6.14606', 'vk6.15306', 'vk6.15433', 'vk6.16225', 'vk6.17971', 'vk6.24409', 'vk6.30175', 'vk6.30249', 'vk6.30346', 'vk6.30471', 'vk6.33948', 'vk6.34353', 'vk6.34409', 'vk6.43836', 'vk6.50441', 'vk6.50472', 'vk6.54194', 'vk6.63445'] |
| 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 | O1O2O3U1O4U5U4U3O6O5U6U2 |
| R3 orbit | {'O1O2O3U1O4U5U4U3O6O5U6U2'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U2U4O5O4U1U6U5O6U3 |
| Gauss code of K* | O1O2O3U4U1O4O5U6U5U3O6U2 |
| Gauss code of -K* | O1O2O3U2O4U1U5U4O5O6U3U6 |
| 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 1 -1 -1],[ 2 0 2 1 0 1 0],[-1 -2 0 1 1 -2 -1],[-2 -1 -1 0 0 -3 -1],[-1 0 -1 0 0 -1 -1],[ 1 -1 2 3 1 0 -1],[ 1 0 1 1 1 1 0]] |
| Primitive based matrix | [[ 0 2 1 1 -1 -1 -2],[-2 0 0 -1 -1 -3 -1],[-1 0 0 -1 -1 -1 0],[-1 1 1 0 -1 -2 -2],[ 1 1 1 1 0 1 0],[ 1 3 1 2 -1 0 -1],[ 2 1 0 2 0 1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,-1,1,1,2,0,1,1,3,1,1,1,1,0,1,2,2,-1,0,1] |
| Phi over symmetry | [-2,-1,-1,1,1,2,0,1,0,2,1,1,1,1,1,1,2,3,-1,0,1] |
| Phi of -K | [-2,-1,-1,1,1,2,0,1,1,3,3,1,0,1,0,1,1,2,-1,0,1] |
| Phi of K* | [-2,-1,-1,1,1,2,0,1,0,2,3,1,0,1,1,1,1,3,-1,0,1] |
| Phi of -K* | [-2,-1,-1,1,1,2,0,1,0,2,1,1,1,1,1,1,2,3,-1,0,1] |
| Symmetry type of based matrix | c |
| u-polynomial | 0 |
| Normalized Jones-Krushkal polynomial | 6z^2+27z+31 |
| Enhanced Jones-Krushkal polynomial | 6w^3z^2+27w^2z+31w |
| Inner characteristic polynomial | t^6+26t^4+32t^2+4 |
| Outer characteristic polynomial | t^7+38t^5+56t^3+11t |
| Flat arrow polynomial | 4*K1**3 - 4*K1**2 - 4*K1*K2 - K1 + 2*K2 + K3 + 3 |
| 2-strand cable arrow polynomial | 2528*K1**4*K2 - 5152*K1**4 + 864*K1**3*K2*K3 - 1120*K1**3*K3 - 128*K1**2*K2**4 + 1056*K1**2*K2**3 + 128*K1**2*K2**2*K4 - 8496*K1**2*K2**2 - 544*K1**2*K2*K4 + 10584*K1**2*K2 - 640*K1**2*K3**2 - 32*K1**2*K4**2 - 4280*K1**2 + 416*K1*K2**3*K3 - 1504*K1*K2**2*K3 - 192*K1*K2**2*K5 - 32*K1*K2*K3*K4 + 7552*K1*K2*K3 + 768*K1*K3*K4 + 32*K1*K4*K5 - 32*K2**6 + 64*K2**4*K4 - 880*K2**4 - 32*K2**3*K6 - 208*K2**2*K3**2 - 16*K2**2*K4**2 + 1016*K2**2*K4 - 3910*K2**2 + 104*K2*K3*K5 + 16*K2*K4*K6 - 1692*K3**2 - 248*K4**2 - 12*K5**2 - 2*K6**2 + 4022 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{2, 6}, {4, 5}, {1, 3}], [{4, 6}, {2, 5}, {1, 3}]] |
| If K is slice | False |