| Min(phi) over symmetries of the knot is: [-3,-2,-1,1,2,3,0,1,3,2,4,0,2,1,2,1,1,2,1,2,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.742'] |
| Arrow polynomial of the knot is: -12*K1**2 - 4*K1*K2 + 2*K1 + 6*K2 + 2*K3 + 7 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.546', '6.591', '6.598', '6.666', '6.680', '6.742', '6.778', '6.805', '6.822', '6.824', '6.1129', '6.1512', '6.1647', '6.1678', '6.1705', '6.1847', '6.1857'] |
| Outer characteristic polynomial of the knot is: t^7+78t^5+47t^3+4t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.742'] |
| 2-strand cable arrow polynomial of the knot is: -64*K1**6 - 64*K1**4*K2**2 + 576*K1**4*K2 - 3328*K1**4 + 288*K1**3*K2*K3 - 896*K1**3*K3 + 96*K1**2*K2**2*K4 - 2976*K1**2*K2**2 - 544*K1**2*K2*K4 + 7704*K1**2*K2 - 832*K1**2*K3**2 - 32*K1**2*K3*K5 - 128*K1**2*K4**2 - 4708*K1**2 - 352*K1*K2**2*K3 - 96*K1*K2**2*K5 - 96*K1*K2*K3*K4 + 5832*K1*K2*K3 + 1432*K1*K3*K4 + 200*K1*K4*K5 + 16*K1*K5*K6 - 304*K2**4 - 96*K2**2*K3**2 - 16*K2**2*K4**2 + 856*K2**2*K4 - 4036*K2**2 + 192*K2*K3*K5 + 16*K2*K4*K6 - 2020*K3**2 - 664*K4**2 - 104*K5**2 - 12*K6**2 + 4158 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.742'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.20001', 'vk6.20086', 'vk6.21271', 'vk6.21368', 'vk6.27048', 'vk6.27147', 'vk6.28751', 'vk6.28836', 'vk6.38449', 'vk6.38552', 'vk6.40636', 'vk6.40749', 'vk6.45329', 'vk6.45448', 'vk6.47096', 'vk6.47190', 'vk6.56816', 'vk6.56891', 'vk6.57948', 'vk6.58029', 'vk6.61330', 'vk6.61417', 'vk6.62504', 'vk6.62574', 'vk6.66536', 'vk6.66599', 'vk6.67323', 'vk6.67390', 'vk6.69178', 'vk6.69247', 'vk6.69927', 'vk6.69988'] |
| 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 | O1O2O3O4U2O5U1U6U3O6U5U4 |
| R3 orbit | {'O1O2O3O4U2O5U1U6U3O6U5U4'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U1U5O6U2U6U4O5U3 |
| Gauss code of K* | O1O2O3U2O4O5U1U6U3U5O6U4 |
| Gauss code of -K* | O1O2O3U4O5U6U1U5U3O6O4U2 |
| 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 1 3 2 -1],[ 3 0 0 2 4 2 2],[ 2 0 0 1 2 1 1],[-1 -2 -1 0 1 0 -1],[-3 -4 -2 -1 0 0 -3],[-2 -2 -1 0 0 0 -2],[ 1 -2 -1 1 3 2 0]] |
| Primitive based matrix | [[ 0 3 2 1 -1 -2 -3],[-3 0 0 -1 -3 -2 -4],[-2 0 0 0 -2 -1 -2],[-1 1 0 0 -1 -1 -2],[ 1 3 2 1 0 -1 -2],[ 2 2 1 1 1 0 0],[ 3 4 2 2 2 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-3,-2,-1,1,2,3,0,1,3,2,4,0,2,1,2,1,1,2,1,2,0] |
| Phi over symmetry | [-3,-2,-1,1,2,3,0,1,3,2,4,0,2,1,2,1,1,2,1,2,0] |
| Phi of -K | [-3,-2,-1,1,2,3,1,0,2,3,2,0,2,3,3,1,1,1,1,1,1] |
| Phi of K* | [-3,-2,-1,1,2,3,1,1,1,3,2,1,1,3,3,1,2,2,0,0,1] |
| Phi of -K* | [-3,-2,-1,1,2,3,0,2,2,2,4,1,1,1,2,1,2,3,0,1,0] |
| Symmetry type of based matrix | c |
| u-polynomial | 0 |
| Normalized Jones-Krushkal polynomial | 17z+35 |
| Enhanced Jones-Krushkal polynomial | 17w^2z+35w |
| Inner characteristic polynomial | t^6+50t^4+19t^2 |
| Outer characteristic polynomial | t^7+78t^5+47t^3+4t |
| Flat arrow polynomial | -12*K1**2 - 4*K1*K2 + 2*K1 + 6*K2 + 2*K3 + 7 |
| 2-strand cable arrow polynomial | -64*K1**6 - 64*K1**4*K2**2 + 576*K1**4*K2 - 3328*K1**4 + 288*K1**3*K2*K3 - 896*K1**3*K3 + 96*K1**2*K2**2*K4 - 2976*K1**2*K2**2 - 544*K1**2*K2*K4 + 7704*K1**2*K2 - 832*K1**2*K3**2 - 32*K1**2*K3*K5 - 128*K1**2*K4**2 - 4708*K1**2 - 352*K1*K2**2*K3 - 96*K1*K2**2*K5 - 96*K1*K2*K3*K4 + 5832*K1*K2*K3 + 1432*K1*K3*K4 + 200*K1*K4*K5 + 16*K1*K5*K6 - 304*K2**4 - 96*K2**2*K3**2 - 16*K2**2*K4**2 + 856*K2**2*K4 - 4036*K2**2 + 192*K2*K3*K5 + 16*K2*K4*K6 - 2020*K3**2 - 664*K4**2 - 104*K5**2 - 12*K6**2 + 4158 |
| Genus of based matrix | 0 |
| Fillings of based matrix | [[{3, 6}, {2, 5}, {1, 4}]] |
| If K is slice | True |