| Min(phi) over symmetries of the knot is: [-2,-1,-1,1,1,2,-1,1,2,2,2,1,1,1,0,0,1,1,0,0,1] |
| Flat knots (up to 7 crossings) with same phi are :['6.1071'] |
| Arrow polynomial of the knot is: -4*K1**2 - 4*K1*K2 + 2*K1 + 2*K2 + 2*K3 + 3 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.65', '6.137', '6.201', '6.203', '6.214', '6.310', '6.314', '6.332', '6.385', '6.386', '6.401', '6.516', '6.564', '6.571', '6.572', '6.578', '6.621', '6.626', '6.716', '6.773', '6.807', '6.814', '6.821', '6.940', '6.966', '6.1036', '6.1071', '6.1108', '6.1111', '6.1131', '6.1188', '6.1203', '6.1206', '6.1220', '6.1340', '6.1387', '6.1548', '6.1663', '6.1680', '6.1693', '6.1831', '6.1932'] |
| Outer characteristic polynomial of the knot is: t^7+32t^5+57t^3+6t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1071'] |
| 2-strand cable arrow polynomial of the knot is: -816*K1**4 + 800*K1**3*K2*K3 + 32*K1**3*K3*K4 - 1024*K1**3*K3 - 2496*K1**2*K2**2 + 256*K1**2*K2*K3**2 - 672*K1**2*K2*K4 + 6048*K1**2*K2 - 1360*K1**2*K3**2 - 48*K1**2*K4**2 - 5584*K1**2 + 192*K1*K2**3*K3 - 832*K1*K2**2*K3 - 128*K1*K2**2*K5 - 384*K1*K2*K3*K4 + 6672*K1*K2*K3 + 1632*K1*K3*K4 + 88*K1*K4*K5 - 208*K2**4 - 352*K2**2*K3**2 - 48*K2**2*K4**2 + 856*K2**2*K4 - 4028*K2**2 + 304*K2*K3*K5 + 32*K2*K4*K6 - 2300*K3**2 - 560*K4**2 - 28*K5**2 - 4*K6**2 + 3958 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1071'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.11019', 'vk6.11098', 'vk6.12187', 'vk6.12294', 'vk6.18197', 'vk6.18534', 'vk6.24653', 'vk6.25081', 'vk6.30586', 'vk6.30681', 'vk6.31854', 'vk6.31901', 'vk6.36785', 'vk6.37237', 'vk6.44026', 'vk6.44368', 'vk6.51830', 'vk6.51897', 'vk6.52700', 'vk6.52794', 'vk6.55992', 'vk6.56266', 'vk6.60524', 'vk6.60868', 'vk6.63507', 'vk6.63552', 'vk6.63987', 'vk6.64032', 'vk6.65651', 'vk6.65932', 'vk6.68696', 'vk6.68907'] |
| 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 | O1O2O3O4U5U4O6U1O5U2U6U3 |
| R3 orbit | {'O1O2O3O4U5U4O6U1O5U2U6U3'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U2U5U3O6U4O5U1U6 |
| Gauss code of K* | O1O2O3U4U1U3U5O6O5U2O4U6 |
| Gauss code of -K* | O1O2O3U4O5U2O6O4U6U1U3U5 |
| 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 0 2 0 1 1],[ 1 0 0 2 1 0 0],[-2 -2 -2 0 1 -2 -1],[-1 0 -1 -1 0 -1 -1],[ 1 -1 0 2 1 0 1],[-1 -1 0 1 1 -1 0]] |
| Primitive based matrix | [[ 0 2 1 1 -1 -1 -2],[-2 0 1 -1 -2 -2 -2],[-1 -1 0 -1 -1 -1 0],[-1 1 1 0 0 -1 -1],[ 1 2 1 0 0 0 0],[ 1 2 1 1 0 0 -1],[ 2 2 0 1 0 1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,-1,1,1,2,-1,1,2,2,2,1,1,1,0,0,1,1,0,0,1] |
| Phi over symmetry | [-2,-1,-1,1,1,2,-1,1,2,2,2,1,1,1,0,0,1,1,0,0,1] |
| Phi of -K | [-2,-1,-1,1,1,2,0,1,2,3,2,0,1,1,1,2,1,1,-1,0,2] |
| Phi of K* | [-2,-1,-1,1,1,2,0,2,1,1,2,1,1,2,2,1,1,3,0,0,1] |
| Phi of -K* | [-2,-1,-1,1,1,2,0,1,0,1,2,0,1,0,2,1,1,2,-1,-1,1] |
| Symmetry type of based matrix | c |
| u-polynomial | 0 |
| Normalized Jones-Krushkal polynomial | 5z^2+24z+29 |
| Enhanced Jones-Krushkal polynomial | 5w^3z^2+24w^2z+29w |
| Inner characteristic polynomial | t^6+20t^4+23t^2+1 |
| Outer characteristic polynomial | t^7+32t^5+57t^3+6t |
| Flat arrow polynomial | -4*K1**2 - 4*K1*K2 + 2*K1 + 2*K2 + 2*K3 + 3 |
| 2-strand cable arrow polynomial | -816*K1**4 + 800*K1**3*K2*K3 + 32*K1**3*K3*K4 - 1024*K1**3*K3 - 2496*K1**2*K2**2 + 256*K1**2*K2*K3**2 - 672*K1**2*K2*K4 + 6048*K1**2*K2 - 1360*K1**2*K3**2 - 48*K1**2*K4**2 - 5584*K1**2 + 192*K1*K2**3*K3 - 832*K1*K2**2*K3 - 128*K1*K2**2*K5 - 384*K1*K2*K3*K4 + 6672*K1*K2*K3 + 1632*K1*K3*K4 + 88*K1*K4*K5 - 208*K2**4 - 352*K2**2*K3**2 - 48*K2**2*K4**2 + 856*K2**2*K4 - 4028*K2**2 + 304*K2*K3*K5 + 32*K2*K4*K6 - 2300*K3**2 - 560*K4**2 - 28*K5**2 - 4*K6**2 + 3958 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{2, 6}, {4, 5}, {1, 3}], [{5, 6}, {2, 4}, {1, 3}]] |
| If K is slice | False |