| Min(phi) over symmetries of the knot is: [-3,-2,0,0,2,3,-1,0,2,2,4,1,2,1,2,0,0,1,1,2,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.575'] |
| Arrow polynomial of the knot is: 8*K1**3 - 4*K1**2 - 4*K1*K2 - 4*K1 + 2*K2 + 3 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.206', '6.236', '6.575', '6.580', '6.613', '6.619', '6.810', '6.819', '6.831', '6.838', '6.957', '6.1018', '6.1028', '6.1046', '6.1073', '6.1279', '6.1507', '6.1532', '6.1556', '6.1639', '6.1688', '6.1924', '6.1931'] |
| Outer characteristic polynomial of the knot is: t^7+83t^5+71t^3+9t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.575'] |
| 2-strand cable arrow polynomial of the knot is: -128*K1**4*K2**2 + 1216*K1**4*K2 - 3392*K1**4 + 160*K1**3*K2*K3 - 896*K1**3*K3 + 384*K1**2*K2**5 - 1152*K1**2*K2**4 + 3136*K1**2*K2**3 - 64*K1**2*K2**2*K3**2 - 8624*K1**2*K2**2 + 64*K1**2*K2*K3**2 - 640*K1**2*K2*K4 + 10136*K1**2*K2 - 224*K1**2*K3**2 - 4892*K1**2 + 1120*K1*K2**3*K3 + 128*K1*K2**2*K3*K4 - 1536*K1*K2**2*K3 - 64*K1*K2**2*K5 - 192*K1*K2*K3*K4 + 6800*K1*K2*K3 + 328*K1*K3*K4 - 320*K2**6 + 96*K2**4*K4 - 2288*K2**4 - 608*K2**2*K3**2 - 64*K2**2*K4**2 + 1560*K2**2*K4 - 2584*K2**2 + 216*K2*K3*K5 - 1276*K3**2 - 112*K4**2 + 3710 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.575'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.73706', 'vk6.73825', 'vk6.74197', 'vk6.74809', 'vk6.75631', 'vk6.75818', 'vk6.76362', 'vk6.76872', 'vk6.78610', 'vk6.78807', 'vk6.79230', 'vk6.79705', 'vk6.80248', 'vk6.80387', 'vk6.80711', 'vk6.81071', 'vk6.81606', 'vk6.81788', 'vk6.81927', 'vk6.82175', 'vk6.82295', 'vk6.82653', 'vk6.83197', 'vk6.84057', 'vk6.84206', 'vk6.84694', 'vk6.85013', 'vk6.86007', 'vk6.87767', 'vk6.88200', 'vk6.89405', 'vk6.89596'] |
| 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 | O1O2O3O4U1O5U2O6U5U3U4U6 |
| R3 orbit | {'O1O2O3O4U1O5U2O6U5U3U4U6'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U5U1U2U6O5U3O6U4 |
| Gauss code of K* | O1O2O3O4U5U6U2U3O5U1O6U4 |
| Gauss code of -K* | O1O2O3O4U1O5U4O6U2U3U5U6 |
| 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 0 2 0 3],[ 3 0 1 2 3 1 2],[ 2 -1 0 2 3 1 3],[ 0 -2 -2 0 1 0 3],[-2 -3 -3 -1 0 0 2],[ 0 -1 -1 0 0 0 1],[-3 -2 -3 -3 -2 -1 0]] |
| Primitive based matrix | [[ 0 3 2 0 0 -2 -3],[-3 0 -2 -1 -3 -3 -2],[-2 2 0 0 -1 -3 -3],[ 0 1 0 0 0 -1 -1],[ 0 3 1 0 0 -2 -2],[ 2 3 3 1 2 0 -1],[ 3 2 3 1 2 1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-3,-2,0,0,2,3,2,1,3,3,2,0,1,3,3,0,1,1,2,2,1] |
| Phi over symmetry | [-3,-2,0,0,2,3,-1,0,2,2,4,1,2,1,2,0,0,1,1,2,0] |
| Phi of -K | [-3,-2,0,0,2,3,0,1,2,2,4,0,1,1,2,0,1,0,2,2,-1] |
| Phi of K* | [-3,-2,0,0,2,3,-1,0,2,2,4,1,2,1,2,0,0,1,1,2,0] |
| Phi of -K* | [-3,-2,0,0,2,3,1,1,2,3,2,1,2,3,3,0,0,1,1,3,2] |
| Symmetry type of based matrix | c |
| u-polynomial | 0 |
| Normalized Jones-Krushkal polynomial | 5z^2+24z+29 |
| Enhanced Jones-Krushkal polynomial | -2w^4z^2+7w^3z^2+24w^2z+29w |
| Inner characteristic polynomial | t^6+57t^4+23t^2 |
| Outer characteristic polynomial | t^7+83t^5+71t^3+9t |
| Flat arrow polynomial | 8*K1**3 - 4*K1**2 - 4*K1*K2 - 4*K1 + 2*K2 + 3 |
| 2-strand cable arrow polynomial | -128*K1**4*K2**2 + 1216*K1**4*K2 - 3392*K1**4 + 160*K1**3*K2*K3 - 896*K1**3*K3 + 384*K1**2*K2**5 - 1152*K1**2*K2**4 + 3136*K1**2*K2**3 - 64*K1**2*K2**2*K3**2 - 8624*K1**2*K2**2 + 64*K1**2*K2*K3**2 - 640*K1**2*K2*K4 + 10136*K1**2*K2 - 224*K1**2*K3**2 - 4892*K1**2 + 1120*K1*K2**3*K3 + 128*K1*K2**2*K3*K4 - 1536*K1*K2**2*K3 - 64*K1*K2**2*K5 - 192*K1*K2*K3*K4 + 6800*K1*K2*K3 + 328*K1*K3*K4 - 320*K2**6 + 96*K2**4*K4 - 2288*K2**4 - 608*K2**2*K3**2 - 64*K2**2*K4**2 + 1560*K2**2*K4 - 2584*K2**2 + 216*K2*K3*K5 - 1276*K3**2 - 112*K4**2 + 3710 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {3, 5}, {2, 4}], [{2, 6}, {4, 5}, {1, 3}], [{5, 6}, {1, 4}, {2, 3}], [{5, 6}, {1, 4}, {3}, {2}]] |
| If K is slice | False |