| Min(phi) over symmetries of the knot is: [-3,-1,-1,1,2,2,0,2,2,2,3,1,1,0,1,1,2,2,0,0,-1] |
| Flat knots (up to 7 crossings) with same phi are :['6.658'] |
| Arrow polynomial of the knot is: -8*K1**2 - 2*K1*K2 + K1 + 4*K2 + K3 + 5 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.377', '6.638', '6.646', '6.647', '6.657', '6.658', '6.662', '6.692', '6.695', '6.714', '6.720', '6.726', '6.730', '6.731', '6.749', '6.756', '6.772', '6.779', '6.781', '6.800', '6.829', '6.1085', '6.1089', '6.1302', '6.1349', '6.1350', '6.1360', '6.1362', '6.1375', '6.1384'] |
| Outer characteristic polynomial of the knot is: t^7+62t^5+39t^3+4t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.658'] |
| 2-strand cable arrow polynomial of the knot is: -64*K1**6 - 64*K1**4*K2**2 + 896*K1**4*K2 - 4848*K1**4 + 192*K1**3*K2*K3 - 608*K1**3*K3 - 2512*K1**2*K2**2 - 96*K1**2*K2*K4 + 7744*K1**2*K2 - 336*K1**2*K3**2 - 2716*K1**2 - 128*K1*K2**2*K3 - 32*K1*K2*K3*K4 + 3072*K1*K2*K3 + 336*K1*K3*K4 + 16*K1*K4*K5 - 160*K2**4 - 80*K2**2*K3**2 - 8*K2**2*K4**2 + 232*K2**2*K4 - 2822*K2**2 + 64*K2*K3*K5 + 8*K2*K4*K6 - 824*K3**2 - 124*K4**2 - 12*K5**2 - 2*K6**2 + 2874 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.658'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.20000', 'vk6.20084', 'vk6.21272', 'vk6.21366', 'vk6.27047', 'vk6.27149', 'vk6.28752', 'vk6.28838', 'vk6.38448', 'vk6.38550', 'vk6.40637', 'vk6.40747', 'vk6.45328', 'vk6.45450', 'vk6.47097', 'vk6.47192', 'vk6.56815', 'vk6.56889', 'vk6.57949', 'vk6.58027', 'vk6.61329', 'vk6.61419', 'vk6.62505', 'vk6.62576', 'vk6.66535', 'vk6.66597', 'vk6.67324', 'vk6.67388', 'vk6.69177', 'vk6.69249', 'vk6.69928', 'vk6.69990'] |
| 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 | O1O2O3O4U2O5U3U1O6U4U6U5 |
| R3 orbit | {'O1O2O3O4U2O5U3U1O6U4U6U5'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U5U6U1O6U4U2O5U3 |
| Gauss code of K* | O1O2O3U4U5U6U1O5U3O6O4U2 |
| Gauss code of -K* | O1O2O3U2O4O5U1O6U3U5U6U4 |
| 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 -2 -1 1 3 1],[ 2 0 -1 1 3 3 1],[ 2 1 0 1 2 2 1],[ 1 -1 -1 0 1 2 1],[-1 -3 -2 -1 0 2 1],[-3 -3 -2 -2 -2 0 0],[-1 -1 -1 -1 -1 0 0]] |
| Primitive based matrix | [[ 0 3 1 1 -1 -2 -2],[-3 0 0 -2 -2 -2 -3],[-1 0 0 -1 -1 -1 -1],[-1 2 1 0 -1 -2 -3],[ 1 2 1 1 0 -1 -1],[ 2 2 1 2 1 0 1],[ 2 3 1 3 1 -1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-3,-1,-1,1,2,2,0,2,2,2,3,1,1,1,1,1,2,3,1,1,-1] |
| Phi over symmetry | [-3,-1,-1,1,2,2,0,2,2,2,3,1,1,0,1,1,2,2,0,0,-1] |
| Phi of -K | [-2,-2,-1,1,1,3,-1,0,1,2,3,0,0,2,2,1,1,2,-1,0,2] |
| Phi of K* | [-3,-1,-1,1,2,2,0,2,2,2,3,1,1,0,1,1,2,2,0,0,-1] |
| Phi of -K* | [-2,-2,-1,1,1,3,-1,1,1,3,3,1,1,2,2,1,1,2,-1,0,2] |
| Symmetry type of based matrix | c |
| u-polynomial | -t^3+2t^2-t |
| Normalized Jones-Krushkal polynomial | 17z+35 |
| Enhanced Jones-Krushkal polynomial | 17w^2z+35w |
| Inner characteristic polynomial | t^6+42t^4+15t^2 |
| Outer characteristic polynomial | t^7+62t^5+39t^3+4t |
| Flat arrow polynomial | -8*K1**2 - 2*K1*K2 + K1 + 4*K2 + K3 + 5 |
| 2-strand cable arrow polynomial | -64*K1**6 - 64*K1**4*K2**2 + 896*K1**4*K2 - 4848*K1**4 + 192*K1**3*K2*K3 - 608*K1**3*K3 - 2512*K1**2*K2**2 - 96*K1**2*K2*K4 + 7744*K1**2*K2 - 336*K1**2*K3**2 - 2716*K1**2 - 128*K1*K2**2*K3 - 32*K1*K2*K3*K4 + 3072*K1*K2*K3 + 336*K1*K3*K4 + 16*K1*K4*K5 - 160*K2**4 - 80*K2**2*K3**2 - 8*K2**2*K4**2 + 232*K2**2*K4 - 2822*K2**2 + 64*K2*K3*K5 + 8*K2*K4*K6 - 824*K3**2 - 124*K4**2 - 12*K5**2 - 2*K6**2 + 2874 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {4, 5}, {2, 3}], [{2, 6}, {4, 5}, {1, 3}], [{4, 6}, {3, 5}, {1, 2}], [{4, 6}, {3, 5}, {2}, {1}]] |
| If K is slice | False |