| Min(phi) over symmetries of the knot is: [-2,-1,0,1,1,1,0,0,1,1,2,0,0,1,0,0,1,0,1,0,-1] |
| Flat knots (up to 7 crossings) with same phi are :['6.1484'] |
| Arrow polynomial of the knot is: 4*K1**3 - 6*K1**2 - 4*K1*K2 - K1 + 3*K2 + K3 + 4 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.361', '6.460', '6.555', '6.651', '6.753', '6.782', '6.1029', '6.1197', '6.1200', '6.1232', '6.1236', '6.1278', '6.1281', '6.1343', '6.1380', '6.1385', '6.1389', '6.1484', '6.1492', '6.1493', '6.1527', '6.1533', '6.1550', '6.1553', '6.1557', '6.1576', '6.1578', '6.1582', '6.1586', '6.1674', '6.1698', '6.1754', '6.1759', '6.1775', '6.1791', '6.1798', '6.1800', '6.1805', '6.1822', '6.1826', '6.1839', '6.1844', '6.1845'] |
| Outer characteristic polynomial of the knot is: t^7+36t^5+43t^3+10t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1484'] |
| 2-strand cable arrow polynomial of the knot is: -384*K1**4*K2**2 + 1152*K1**4*K2 - 2176*K1**4 + 480*K1**3*K2*K3 - 736*K1**3*K3 - 192*K1**2*K2**4 + 928*K1**2*K2**3 - 6112*K1**2*K2**2 - 448*K1**2*K2*K4 + 8336*K1**2*K2 - 288*K1**2*K3**2 - 5564*K1**2 + 416*K1*K2**3*K3 - 928*K1*K2**2*K3 - 64*K1*K2**2*K5 - 96*K1*K2*K3*K4 + 7136*K1*K2*K3 + 704*K1*K3*K4 + 24*K1*K4*K5 - 32*K2**6 + 64*K2**4*K4 - 760*K2**4 - 272*K2**2*K3**2 - 48*K2**2*K4**2 + 968*K2**2*K4 - 4094*K2**2 + 160*K2*K3*K5 + 16*K2*K4*K6 - 2052*K3**2 - 386*K4**2 - 24*K5**2 - 2*K6**2 + 4272 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1484'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.11441', 'vk6.11736', 'vk6.12751', 'vk6.13094', 'vk6.20323', 'vk6.21665', 'vk6.27624', 'vk6.29169', 'vk6.31196', 'vk6.31535', 'vk6.32360', 'vk6.32775', 'vk6.39054', 'vk6.41314', 'vk6.45806', 'vk6.47482', 'vk6.52206', 'vk6.52467', 'vk6.53033', 'vk6.53353', 'vk6.57182', 'vk6.58394', 'vk6.61793', 'vk6.62914', 'vk6.63776', 'vk6.63886', 'vk6.64200', 'vk6.64386', 'vk6.66797', 'vk6.67666', 'vk6.69434', 'vk6.70157'] |
| 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 | O1O2O3U1O4U2U5O6O5U3U4U6 |
| R3 orbit | {'O1O2O3U1O4U2U5O6O5U3U4U6'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U4U5U1O6O4U6U2O5U3 |
| Gauss code of K* | O1O2O3U4U5U1O4U2O5O6U3U6 |
| Gauss code of -K* | O1O2O3U4U1O4O5U2O6U3U5U6 |
| 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 0 1 1 1],[ 2 0 1 2 2 2 1],[ 1 -1 0 1 2 1 2],[ 0 -2 -1 0 1 0 1],[-1 -2 -2 -1 0 -1 0],[-1 -2 -1 0 1 0 1],[-1 -1 -2 -1 0 -1 0]] |
| Primitive based matrix | [[ 0 1 1 1 0 -1 -2],[-1 0 1 1 0 -1 -2],[-1 -1 0 0 -1 -2 -1],[-1 -1 0 0 -1 -2 -2],[ 0 0 1 1 0 -1 -2],[ 1 1 2 2 1 0 -1],[ 2 2 1 2 2 1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-1,-1,-1,0,1,2,-1,-1,0,1,2,0,1,2,1,1,2,2,1,2,1] |
| Phi over symmetry | [-2,-1,0,1,1,1,0,0,1,1,2,0,0,1,0,0,1,0,1,0,-1] |
| Phi of -K | [-2,-1,0,1,1,1,0,0,1,1,2,0,0,1,0,0,1,0,1,0,-1] |
| Phi of K* | [-1,-1,-1,0,1,2,-1,0,0,0,1,1,1,1,1,0,0,2,0,0,0] |
| Phi of -K* | [-2,-1,0,1,1,1,1,2,1,2,2,1,2,1,2,1,0,1,-1,0,1] |
| Symmetry type of based matrix | c |
| u-polynomial | t^2-2t |
| Normalized Jones-Krushkal polynomial | 5z^2+26z+33 |
| Enhanced Jones-Krushkal polynomial | 5w^3z^2+26w^2z+33w |
| Inner characteristic polynomial | t^6+28t^4+16t^2 |
| Outer characteristic polynomial | t^7+36t^5+43t^3+10t |
| Flat arrow polynomial | 4*K1**3 - 6*K1**2 - 4*K1*K2 - K1 + 3*K2 + K3 + 4 |
| 2-strand cable arrow polynomial | -384*K1**4*K2**2 + 1152*K1**4*K2 - 2176*K1**4 + 480*K1**3*K2*K3 - 736*K1**3*K3 - 192*K1**2*K2**4 + 928*K1**2*K2**3 - 6112*K1**2*K2**2 - 448*K1**2*K2*K4 + 8336*K1**2*K2 - 288*K1**2*K3**2 - 5564*K1**2 + 416*K1*K2**3*K3 - 928*K1*K2**2*K3 - 64*K1*K2**2*K5 - 96*K1*K2*K3*K4 + 7136*K1*K2*K3 + 704*K1*K3*K4 + 24*K1*K4*K5 - 32*K2**6 + 64*K2**4*K4 - 760*K2**4 - 272*K2**2*K3**2 - 48*K2**2*K4**2 + 968*K2**2*K4 - 4094*K2**2 + 160*K2*K3*K5 + 16*K2*K4*K6 - 2052*K3**2 - 386*K4**2 - 24*K5**2 - 2*K6**2 + 4272 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{2, 6}, {1, 5}, {3, 4}], [{2, 6}, {3, 5}, {1, 4}], [{2, 6}, {4, 5}, {1, 3}]] |
| If K is slice | False |