| Min(phi) over symmetries of the knot is: [-3,-1,0,1,1,2,0,2,3,3,2,2,1,1,1,0,1,1,0,2,1] |
| Flat knots (up to 7 crossings) with same phi are :['6.644'] |
| Arrow polynomial of the knot is: -6*K1**2 - 2*K1*K2 + K1 + 3*K2 + K3 + 4 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.323', '6.380', '6.444', '6.472', '6.523', '6.579', '6.592', '6.595', '6.609', '6.614', '6.620', '6.644', '6.648', '6.669', '6.671', '6.681', '6.693', '6.724', '6.725', '6.757', '6.766', '6.785', '6.786', '6.797', '6.798', '6.816', '6.833', '6.972', '6.978', '6.1056', '6.1064', '6.1066', '6.1087', '6.1094', '6.1273', '6.1277', '6.1282', '6.1295', '6.1300', '6.1313', '6.1344', '6.1353', '6.1354'] |
| Outer characteristic polynomial of the knot is: t^7+42t^5+73t^3+7t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.644'] |
| 2-strand cable arrow polynomial of the knot is: -64*K1**6 + 256*K1**4*K2 - 3568*K1**4 + 32*K1**3*K2*K3 - 32*K1**3*K3 + 288*K1**2*K2**3 - 4880*K1**2*K2**2 + 64*K1**2*K2*K3**2 - 64*K1**2*K2*K4 + 7384*K1**2*K2 - 1648*K1**2*K3**2 - 48*K1**2*K4**2 - 3260*K1**2 - 448*K1*K2**2*K3 - 128*K1*K2*K3*K4 + 6224*K1*K2*K3 + 1760*K1*K3*K4 + 40*K1*K4*K5 - 408*K2**4 - 176*K2**2*K3**2 - 8*K2**2*K4**2 + 568*K2**2*K4 - 3182*K2**2 + 200*K2*K3*K5 + 8*K2*K4*K6 - 1892*K3**2 - 542*K4**2 - 40*K5**2 - 2*K6**2 + 3564 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.644'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.4061', 'vk6.4094', 'vk6.5299', 'vk6.5332', 'vk6.7429', 'vk6.7454', 'vk6.8922', 'vk6.8955', 'vk6.10121', 'vk6.10290', 'vk6.10315', 'vk6.14555', 'vk6.15267', 'vk6.15394', 'vk6.15773', 'vk6.16190', 'vk6.29869', 'vk6.29902', 'vk6.33909', 'vk6.33992', 'vk6.34222', 'vk6.34377', 'vk6.48462', 'vk6.49162', 'vk6.50209', 'vk6.50236', 'vk6.51597', 'vk6.53960', 'vk6.54023', 'vk6.54189', 'vk6.54465', 'vk6.63316'] |
| 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 | O1O2O3O4U1O5U4U5O6U2U6U3 |
| R3 orbit | {'O1O2O3O4U1O5U4U5O6U2U6U3'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U2U5U3O5U6U1O6U4 |
| Gauss code of K* | O1O2O3U4U1U3U5O4U6O5O6U2 |
| Gauss code of -K* | O1O2O3U2O4O5U4O6U5U1U3U6 |
| 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 -1 2 0 1 1],[ 3 0 2 3 1 1 1],[ 1 -2 0 2 -1 1 1],[-2 -3 -2 0 -1 1 0],[ 0 -1 1 1 0 1 0],[-1 -1 -1 -1 -1 0 0],[-1 -1 -1 0 0 0 0]] |
| Primitive based matrix | [[ 0 2 1 1 0 -1 -3],[-2 0 1 0 -1 -2 -3],[-1 -1 0 0 -1 -1 -1],[-1 0 0 0 0 -1 -1],[ 0 1 1 0 0 1 -1],[ 1 2 1 1 -1 0 -2],[ 3 3 1 1 1 2 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,-1,0,1,3,-1,0,1,2,3,0,1,1,1,0,1,1,-1,1,2] |
| Phi over symmetry | [-3,-1,0,1,1,2,0,2,3,3,2,2,1,1,1,0,1,1,0,2,1] |
| Phi of -K | [-3,-1,0,1,1,2,0,2,3,3,2,2,1,1,1,0,1,1,0,2,1] |
| Phi of K* | [-2,-1,-1,0,1,3,1,2,1,1,2,0,1,1,3,0,1,3,2,2,0] |
| Phi of -K* | [-3,-1,0,1,1,2,2,1,1,1,3,-1,1,1,2,0,1,1,0,0,-1] |
| Symmetry type of based matrix | c |
| u-polynomial | t^3-t^2-t |
| Normalized Jones-Krushkal polynomial | 3z^2+24z+37 |
| Enhanced Jones-Krushkal polynomial | 3w^3z^2+24w^2z+37w |
| Inner characteristic polynomial | t^6+26t^4+26t^2+1 |
| Outer characteristic polynomial | t^7+42t^5+73t^3+7t |
| Flat arrow polynomial | -6*K1**2 - 2*K1*K2 + K1 + 3*K2 + K3 + 4 |
| 2-strand cable arrow polynomial | -64*K1**6 + 256*K1**4*K2 - 3568*K1**4 + 32*K1**3*K2*K3 - 32*K1**3*K3 + 288*K1**2*K2**3 - 4880*K1**2*K2**2 + 64*K1**2*K2*K3**2 - 64*K1**2*K2*K4 + 7384*K1**2*K2 - 1648*K1**2*K3**2 - 48*K1**2*K4**2 - 3260*K1**2 - 448*K1*K2**2*K3 - 128*K1*K2*K3*K4 + 6224*K1*K2*K3 + 1760*K1*K3*K4 + 40*K1*K4*K5 - 408*K2**4 - 176*K2**2*K3**2 - 8*K2**2*K4**2 + 568*K2**2*K4 - 3182*K2**2 + 200*K2*K3*K5 + 8*K2*K4*K6 - 1892*K3**2 - 542*K4**2 - 40*K5**2 - 2*K6**2 + 3564 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {3, 5}, {2, 4}], [{5, 6}, {2, 4}, {1, 3}]] |
| If K is slice | False |