| Min(phi) over symmetries of the knot is: [-2,-2,0,1,1,2,0,1,0,1,2,1,1,1,3,1,1,2,1,1,-1] |
| Flat knots (up to 7 crossings) with same phi are :['6.960'] |
| Arrow polynomial of the knot is: -2*K1**2 + K2 + 2 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['4.6', '4.8', '6.780', '6.804', '6.914', '6.931', '6.946', '6.960', '6.1002', '6.1016', '6.1019', '6.1051', '6.1058', '6.1078', '6.1102', '6.1115', '6.1217', '6.1294', '6.1306', '6.1317', '6.1321', '6.1324', '6.1336', '6.1377', '6.1416', '6.1420', '6.1427', '6.1429', '6.1434', '6.1436', '6.1437', '6.1439', '6.1441', '6.1444', '6.1450', '6.1451', '6.1458', '6.1459', '6.1477', '6.1482', '6.1490', '6.1503', '6.1504', '6.1511', '6.1521', '6.1547', '6.1560', '6.1561', '6.1562', '6.1597', '6.1598', '6.1600', '6.1601', '6.1608', '6.1620', '6.1622', '6.1624', '6.1634', '6.1635', '6.1637', '6.1638', '6.1713', '6.1725', '6.1758', '6.1846', '6.1933', '6.1944', '6.1949', '6.1950', '6.1951'] |
| Outer characteristic polynomial of the knot is: t^7+41t^5+92t^3+5t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.960'] |
| 2-strand cable arrow polynomial of the knot is: -64*K1**4 + 96*K1**3*K2*K3 - 64*K1**3*K3 + 224*K1**2*K2**2*K4 - 2048*K1**2*K2**2 - 288*K1**2*K2*K4 + 3592*K1**2*K2 - 64*K1**2*K3**2 - 192*K1**2*K4**2 - 3568*K1**2 - 864*K1*K2**2*K3 - 160*K1*K2**2*K5 - 160*K1*K2*K3*K4 + 3576*K1*K2*K3 + 1080*K1*K3*K4 + 344*K1*K4*K5 + 16*K1*K5*K6 - 440*K2**4 - 64*K2**2*K3**2 - 32*K2**2*K4**2 + 1264*K2**2*K4 - 2792*K2**2 + 192*K2*K3*K5 + 48*K2*K4*K6 - 1424*K3**2 - 830*K4**2 - 160*K5**2 - 24*K6**2 + 2804 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.960'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.4234', 'vk6.4313', 'vk6.5503', 'vk6.5619', 'vk6.7606', 'vk6.7695', 'vk6.9099', 'vk6.9178', 'vk6.18374', 'vk6.18714', 'vk6.24827', 'vk6.25286', 'vk6.37011', 'vk6.37461', 'vk6.44184', 'vk6.44505', 'vk6.48554', 'vk6.48609', 'vk6.49259', 'vk6.49377', 'vk6.50347', 'vk6.50402', 'vk6.51080', 'vk6.51111', 'vk6.56147', 'vk6.56376', 'vk6.60672', 'vk6.61021', 'vk6.65807', 'vk6.66061', 'vk6.68804', 'vk6.69014'] |
| 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 | O1O2O3O4U5U2O6O5U6U1U4U3 |
| R3 orbit | {'O1O2O3O4U5U2O6O5U6U1U4U3'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U2U1U4U5O6O5U3U6 |
| Gauss code of K* | O1O2O3O4U2U5U4U3O6O5U1U6 |
| Gauss code of -K* | O1O2O3O4U5U4O6O5U2U1U6U3 |
| 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 2 0 -1],[ 2 0 1 3 2 2 -1],[ 1 -1 0 1 0 1 -1],[-2 -3 -1 0 0 -1 -1],[-2 -2 0 0 0 -1 -1],[ 0 -2 -1 1 1 0 -1],[ 1 1 1 1 1 1 0]] |
| Primitive based matrix | [[ 0 2 2 0 -1 -1 -2],[-2 0 0 -1 0 -1 -2],[-2 0 0 -1 -1 -1 -3],[ 0 1 1 0 -1 -1 -2],[ 1 0 1 1 0 -1 -1],[ 1 1 1 1 1 0 1],[ 2 2 3 2 1 -1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-2,0,1,1,2,0,1,0,1,2,1,1,1,3,1,1,2,1,1,-1] |
| Phi over symmetry | [-2,-2,0,1,1,2,0,1,0,1,2,1,1,1,3,1,1,2,1,1,-1] |
| Phi of -K | [-2,-1,-1,0,2,2,0,2,0,1,2,1,0,2,3,0,2,2,1,1,0] |
| Phi of K* | [-2,-2,0,1,1,2,0,1,2,2,1,1,2,3,2,0,0,0,1,2,0] |
| Phi of -K* | [-2,-1,-1,0,2,2,-1,1,2,2,3,1,1,1,1,1,0,1,1,1,0] |
| Symmetry type of based matrix | c |
| u-polynomial | -t^2+2t |
| Normalized Jones-Krushkal polynomial | 7z^2+24z+21 |
| Enhanced Jones-Krushkal polynomial | 7w^3z^2+24w^2z+21w |
| Inner characteristic polynomial | t^6+27t^4+29t^2+1 |
| Outer characteristic polynomial | t^7+41t^5+92t^3+5t |
| Flat arrow polynomial | -2*K1**2 + K2 + 2 |
| 2-strand cable arrow polynomial | -64*K1**4 + 96*K1**3*K2*K3 - 64*K1**3*K3 + 224*K1**2*K2**2*K4 - 2048*K1**2*K2**2 - 288*K1**2*K2*K4 + 3592*K1**2*K2 - 64*K1**2*K3**2 - 192*K1**2*K4**2 - 3568*K1**2 - 864*K1*K2**2*K3 - 160*K1*K2**2*K5 - 160*K1*K2*K3*K4 + 3576*K1*K2*K3 + 1080*K1*K3*K4 + 344*K1*K4*K5 + 16*K1*K5*K6 - 440*K2**4 - 64*K2**2*K3**2 - 32*K2**2*K4**2 + 1264*K2**2*K4 - 2792*K2**2 + 192*K2*K3*K5 + 48*K2*K4*K6 - 1424*K3**2 - 830*K4**2 - 160*K5**2 - 24*K6**2 + 2804 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {3, 5}, {2, 4}], [{2, 6}, {1, 5}, {3, 4}]] |
| If K is slice | False |