| Min(phi) over symmetries of the knot is: [-3,-2,0,1,2,2,0,1,1,3,4,0,0,1,2,1,1,1,-1,-1,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.597'] |
| Arrow polynomial of the knot is: 4*K1**3 - 2*K1**2 - 2*K1*K2 - 2*K1 + K2 + 2 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['4.2', '6.303', '6.338', '6.381', '6.432', '6.468', '6.558', '6.583', '6.597', '6.607', '6.634', '6.637', '6.643', '6.654', '6.667', '6.701', '6.709', '6.712', '6.718', '6.728', '6.767', '6.801', '6.825', '6.827', '6.974', '6.994', '6.1042', '6.1061', '6.1069', '6.1181', '6.1271', '6.1286', '6.1287', '6.1289', '6.1297', '6.1337', '6.1355'] |
| Outer characteristic polynomial of the knot is: t^7+59t^5+83t^3+4t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.597'] |
| 2-strand cable arrow polynomial of the knot is: -64*K1**4 + 32*K1**3*K2*K3 - 192*K1**2*K2**4 + 288*K1**2*K2**3 + 128*K1**2*K2**2*K4 - 2608*K1**2*K2**2 - 96*K1**2*K2*K4 + 4136*K1**2*K2 - 64*K1**2*K3**2 - 64*K1**2*K4**2 - 3544*K1**2 + 224*K1*K2**3*K3 - 1056*K1*K2**2*K3 - 96*K1*K2**2*K5 + 3432*K1*K2*K3 + 776*K1*K3*K4 + 24*K1*K4*K5 - 32*K2**6 + 32*K2**4*K4 - 792*K2**4 - 208*K2**2*K3**2 - 8*K2**2*K4**2 + 1248*K2**2*K4 - 2512*K2**2 + 208*K2*K3*K5 - 1200*K3**2 - 542*K4**2 - 56*K5**2 + 2604 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.597'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.4728', 'vk6.5048', 'vk6.6256', 'vk6.6703', 'vk6.8229', 'vk6.8672', 'vk6.9614', 'vk6.9936', 'vk6.20657', 'vk6.22090', 'vk6.28147', 'vk6.29578', 'vk6.39585', 'vk6.41818', 'vk6.46204', 'vk6.47824', 'vk6.48768', 'vk6.48974', 'vk6.49572', 'vk6.49781', 'vk6.50782', 'vk6.50993', 'vk6.51266', 'vk6.51466', 'vk6.57573', 'vk6.58741', 'vk6.62247', 'vk6.63195', 'vk6.67043', 'vk6.67918', 'vk6.69672', 'vk6.70355'] |
| 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 | O1O2O3O4U2O5U1O6U5U6U4U3 |
| R3 orbit | {'O1O2O3O4U2O5U1O6U5U6U4U3'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U2U1U5U6O5U4O6U3 |
| Gauss code of K* | O1O2O3O4U5U6U4U3O6U1O5U2 |
| Gauss code of -K* | O1O2O3O4U3O5U4O6U2U1U6U5 |
| 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 -3 -2 2 2 0 1],[ 3 0 0 4 3 1 1],[ 2 0 0 2 1 0 0],[-2 -4 -2 0 0 -1 1],[-2 -3 -1 0 0 -1 1],[ 0 -1 0 1 1 0 1],[-1 -1 0 -1 -1 -1 0]] |
| Primitive based matrix | [[ 0 2 2 1 0 -2 -3],[-2 0 0 1 -1 -1 -3],[-2 0 0 1 -1 -2 -4],[-1 -1 -1 0 -1 0 -1],[ 0 1 1 1 0 0 -1],[ 2 1 2 0 0 0 0],[ 3 3 4 1 1 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-2,-1,0,2,3,0,-1,1,1,3,-1,1,2,4,1,0,1,0,1,0] |
| Phi over symmetry | [-3,-2,0,1,2,2,0,1,1,3,4,0,0,1,2,1,1,1,-1,-1,0] |
| Phi of -K | [-3,-2,0,1,2,2,1,2,3,1,2,2,3,2,3,0,1,1,2,2,0] |
| Phi of K* | [-2,-2,-1,0,2,3,0,2,1,2,1,2,1,3,2,0,3,3,2,2,1] |
| Phi of -K* | [-3,-2,0,1,2,2,0,1,1,3,4,0,0,1,2,1,1,1,-1,-1,0] |
| Symmetry type of based matrix | c |
| u-polynomial | t^3-t^2-t |
| Normalized Jones-Krushkal polynomial | 7z^2+24z+21 |
| Enhanced Jones-Krushkal polynomial | 7w^3z^2+24w^2z+21w |
| Inner characteristic polynomial | t^6+37t^4+28t^2 |
| Outer characteristic polynomial | t^7+59t^5+83t^3+4t |
| Flat arrow polynomial | 4*K1**3 - 2*K1**2 - 2*K1*K2 - 2*K1 + K2 + 2 |
| 2-strand cable arrow polynomial | -64*K1**4 + 32*K1**3*K2*K3 - 192*K1**2*K2**4 + 288*K1**2*K2**3 + 128*K1**2*K2**2*K4 - 2608*K1**2*K2**2 - 96*K1**2*K2*K4 + 4136*K1**2*K2 - 64*K1**2*K3**2 - 64*K1**2*K4**2 - 3544*K1**2 + 224*K1*K2**3*K3 - 1056*K1*K2**2*K3 - 96*K1*K2**2*K5 + 3432*K1*K2*K3 + 776*K1*K3*K4 + 24*K1*K4*K5 - 32*K2**6 + 32*K2**4*K4 - 792*K2**4 - 208*K2**2*K3**2 - 8*K2**2*K4**2 + 1248*K2**2*K4 - 2512*K2**2 + 208*K2*K3*K5 - 1200*K3**2 - 542*K4**2 - 56*K5**2 + 2604 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {2, 5}, {3, 4}]] |
| If K is slice | False |