| Min(phi) over symmetries of the knot is: [-2,-1,-1,1,1,2,0,1,1,2,1,0,0,1,1,1,2,2,-1,0,1] |
| Flat knots (up to 7 crossings) with same phi are :['6.1340'] |
| 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+26t^3+4t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1340'] |
| 2-strand cable arrow polynomial of the knot is: -384*K1**4*K2**2 + 1952*K1**4*K2 - 4896*K1**4 + 1088*K1**3*K2*K3 - 1280*K1**3*K3 + 416*K1**2*K2**3 - 5376*K1**2*K2**2 - 448*K1**2*K2*K4 + 9000*K1**2*K2 - 1728*K1**2*K3**2 - 192*K1**2*K3*K5 - 4376*K1**2 + 96*K1*K2**3*K3 - 512*K1*K2**2*K3 - 64*K1*K2**2*K5 - 128*K1*K2*K3*K4 + 6808*K1*K2*K3 + 1864*K1*K3*K4 + 264*K1*K4*K5 - 208*K2**4 - 64*K2**2*K3**2 - 16*K2**2*K4**2 + 480*K2**2*K4 - 3980*K2**2 + 352*K2*K3*K5 + 32*K2*K4*K6 + 64*K3**2*K6 - 2248*K3**2 - 620*K4**2 - 208*K5**2 - 44*K6**2 + 4354 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1340'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.4417', 'vk6.4514', 'vk6.5799', 'vk6.5928', 'vk6.7868', 'vk6.7977', 'vk6.9286', 'vk6.9407', 'vk6.10160', 'vk6.10233', 'vk6.10378', 'vk6.17868', 'vk6.17933', 'vk6.18289', 'vk6.18626', 'vk6.24375', 'vk6.25177', 'vk6.30055', 'vk6.30118', 'vk6.36899', 'vk6.37359', 'vk6.43810', 'vk6.44116', 'vk6.44441', 'vk6.48612', 'vk6.50515', 'vk6.50598', 'vk6.51117', 'vk6.51677', 'vk6.55837', 'vk6.56087', 'vk6.65505'] |
| 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 | O1O2O3U1O4O5U4U2U5O6U3U6 |
| R3 orbit | {'O1O2O3U1O4O5U4U2U5O6U3U6'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U4U1O4U5U2U6O5O6U3 |
| Gauss code of K* | O1O2O3U4O5O4U6U2U5O6U1U3 |
| Gauss code of -K* | O1O2O3U1U3O4U5U2U4O6O5U6 |
| 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 1 -1 2 1],[ 2 0 1 2 0 1 1],[ 1 -1 0 2 0 2 1],[-1 -2 -2 0 -1 1 1],[ 1 0 0 1 0 1 0],[-2 -1 -2 -1 -1 0 0],[-1 -1 -1 -1 0 0 0]] |
| Primitive based matrix | [[ 0 2 1 1 -1 -1 -2],[-2 0 0 -1 -1 -2 -1],[-1 0 0 -1 0 -1 -1],[-1 1 1 0 -1 -2 -2],[ 1 1 0 1 0 0 0],[ 1 2 1 2 0 0 -1],[ 2 1 1 2 0 1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,-1,1,1,2,0,1,1,2,1,1,0,1,1,1,2,2,0,0,1] |
| Phi over symmetry | [-2,-1,-1,1,1,2,0,1,1,2,1,0,0,1,1,1,2,2,-1,0,1] |
| Phi of -K | [-2,-1,-1,1,1,2,0,1,1,2,3,0,0,1,1,1,2,2,-1,0,1] |
| Phi of K* | [-2,-1,-1,1,1,2,0,1,1,2,3,1,0,1,1,1,2,2,0,0,1] |
| Phi of -K* | [-2,-1,-1,1,1,2,0,1,1,2,1,0,0,1,1,1,2,2,-1,0,1] |
| Symmetry type of based matrix | c |
| u-polynomial | 0 |
| Normalized Jones-Krushkal polynomial | 3z^2+24z+37 |
| Enhanced Jones-Krushkal polynomial | 3w^3z^2+24w^2z+37w |
| Inner characteristic polynomial | t^6+20t^4+12t^2 |
| Outer characteristic polynomial | t^7+32t^5+26t^3+4t |
| Flat arrow polynomial | -4*K1**2 - 4*K1*K2 + 2*K1 + 2*K2 + 2*K3 + 3 |
| 2-strand cable arrow polynomial | -384*K1**4*K2**2 + 1952*K1**4*K2 - 4896*K1**4 + 1088*K1**3*K2*K3 - 1280*K1**3*K3 + 416*K1**2*K2**3 - 5376*K1**2*K2**2 - 448*K1**2*K2*K4 + 9000*K1**2*K2 - 1728*K1**2*K3**2 - 192*K1**2*K3*K5 - 4376*K1**2 + 96*K1*K2**3*K3 - 512*K1*K2**2*K3 - 64*K1*K2**2*K5 - 128*K1*K2*K3*K4 + 6808*K1*K2*K3 + 1864*K1*K3*K4 + 264*K1*K4*K5 - 208*K2**4 - 64*K2**2*K3**2 - 16*K2**2*K4**2 + 480*K2**2*K4 - 3980*K2**2 + 352*K2*K3*K5 + 32*K2*K4*K6 + 64*K3**2*K6 - 2248*K3**2 - 620*K4**2 - 208*K5**2 - 44*K6**2 + 4354 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{2, 6}, {1, 5}, {3, 4}], [{3, 6}, {1, 5}, {2, 4}], [{3, 6}, {4, 5}, {1, 2}], [{4, 6}, {1, 5}, {2, 3}], [{6}, {1, 5}, {2, 4}, {3}]] |
| If K is slice | False |