| Min(phi) over symmetries of the knot is: [-2,-1,1,2,-1,1,4,-1,1,-1] |
| Flat knots (up to 7 crossings) with same phi are :['6.1396', '7.35320'] |
| Arrow polynomial of the knot is: -8*K1**2 + 4*K2 + 5 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.668', '6.711', '6.777', '6.803', '6.828', '6.1015', '6.1032', '6.1055', '6.1082', '6.1132', '6.1264', '6.1288', '6.1333', '6.1391', '6.1395', '6.1396', '6.1400', '6.1404', '6.1405', '6.1419', '6.1471', '6.1473', '6.1536', '6.1563', '6.1611', '6.1618', '6.1623', '6.1627', '6.1629', '6.1631', '6.1695', '6.1700', '6.1731', '6.1740', '6.1767', '6.1773', '6.1790', '6.1792', '6.1796', '6.1848', '6.1899', '6.1901', '6.1937', '6.1954', '6.1955', '6.1958', '6.1964', '6.1975', '6.1997', '6.1998', '6.1999', '6.2002', '6.2003', '6.2004', '6.2005', '6.2007', '6.2008', '6.2009', '6.2010', '6.2011', '6.2013', '6.2018', '6.2019', '6.2021', '6.2034', '6.2039', '6.2043', '6.2046', '6.2050', '6.2051', '6.2057', '6.2063'] |
| Outer characteristic polynomial of the knot is: t^5+35t^3+8t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1396'] |
| 2-strand cable arrow polynomial of the knot is: 192*K1**4*K2 - 1440*K1**4 + 64*K1**2*K2**3 - 1120*K1**2*K2**2 + 3632*K1**2*K2 - 32*K1**2*K3**2 - 2168*K1**2 + 1168*K1*K2*K3 + 64*K1*K3*K4 - 96*K2**4 + 48*K2**2*K4 - 1552*K2**2 - 360*K3**2 - 32*K4**2 + 1630 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1396'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.72416', 'vk6.72432', 'vk6.72467', 'vk6.72487', 'vk6.72830', 'vk6.72850', 'vk6.72893', 'vk6.74467', 'vk6.74473', 'vk6.75078', 'vk6.76969', 'vk6.77776', 'vk6.77971', 'vk6.79470', 'vk6.79472', 'vk6.79925', 'vk6.79931', 'vk6.80939', 'vk6.87236', 'vk6.89369'] |
| The R3 orbit of minmal crossing diagrams contains: |
| The diagrammatic symmetry type of this knot is -. |
| The reverse -K is |
| The 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 | O1O2O3U1O4U3O5U2O6U5U4U6 |
| R3 orbit | {'O1O2O3U1O4U3O5U2O6U5U4U6'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U4U5U6O4U2O6U1O5U3 |
| Gauss code of K* | O1O2O3U4U5U6O4U2O6U1O5U3 |
| Gauss code of -K* | Same |
| Diagrammatic symmetry type | - |
| Flat genus of the diagram | 2 |
| If K is checkerboard colorable | False |
| If K is almost classical | False |
| Based matrix from Gauss code | [[ 0 -2 -1 0 1 0 2],[ 2 0 2 1 2 1 0],[ 1 -2 0 0 3 1 2],[ 0 -1 0 0 1 0 1],[-1 -2 -3 -1 0 0 2],[ 0 -1 -1 0 0 0 1],[-2 0 -2 -1 -2 -1 0]] |
| Primitive based matrix | [[ 0 2 1 -1 -2],[-2 0 -2 -2 0],[-1 2 0 -3 -2],[ 1 2 3 0 -2],[ 2 0 2 2 0]] |
| If based matrix primitive | False |
| Phi of primitive based matrix | [-2,-1,1,2,2,2,0,3,2,2] |
| Phi over symmetry | [-2,-1,1,2,-1,1,4,-1,1,-1] |
| Phi of -K | [-2,-1,1,2,-1,1,4,-1,1,-1] |
| Phi of K* | [-2,-1,1,2,-1,1,4,-1,1,-1] |
| Phi of -K* | [-2,-1,1,2,2,2,0,3,2,2] |
| Symmetry type of based matrix | - |
| u-polynomial | 0 |
| Normalized Jones-Krushkal polynomial | 13z+27 |
| Enhanced Jones-Krushkal polynomial | 13w^2z+27w |
| Inner characteristic polynomial | t^4+25t^2 |
| Outer characteristic polynomial | t^5+35t^3+8t |
| Flat arrow polynomial | -8*K1**2 + 4*K2 + 5 |
| 2-strand cable arrow polynomial | 192*K1**4*K2 - 1440*K1**4 + 64*K1**2*K2**3 - 1120*K1**2*K2**2 + 3632*K1**2*K2 - 32*K1**2*K3**2 - 2168*K1**2 + 1168*K1*K2*K3 + 64*K1*K3*K4 - 96*K2**4 + 48*K2**2*K4 - 1552*K2**2 - 360*K3**2 - 32*K4**2 + 1630 |
| Genus of based matrix | 0 |
| Fillings of based matrix | [[{1, 6}, {3, 5}, {2, 4}]] |
| If K is slice | True |