| Min(phi) over symmetries of the knot is: [-3,-1,0,1,1,2,0,2,1,3,3,2,1,1,1,0,0,2,-1,0,1] |
| Flat knots (up to 7 crossings) with same phi are :['6.643'] |
| 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+46t^5+104t^3 |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.643'] |
| 2-strand cable arrow polynomial of the knot is: 128*K1**4*K2**3 - 320*K1**4*K2**2 + 352*K1**4*K2 - 416*K1**4 + 32*K1**3*K2*K3 - 640*K1**2*K2**4 + 896*K1**2*K2**3 - 2272*K1**2*K2**2 + 1960*K1**2*K2 - 1160*K1**2 + 544*K1*K2**3*K3 + 1272*K1*K2*K3 + 8*K1*K3*K4 - 32*K2**6 + 32*K2**4*K4 - 520*K2**4 - 160*K2**2*K3**2 - 8*K2**2*K4**2 + 80*K2**2*K4 - 352*K2**2 + 16*K2*K3*K5 - 240*K3**2 - 14*K4**2 + 812 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.643'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.4185', 'vk6.4266', 'vk6.5427', 'vk6.5547', 'vk6.7540', 'vk6.7622', 'vk6.9050', 'vk6.9131', 'vk6.18245', 'vk6.18582', 'vk6.24721', 'vk6.25136', 'vk6.36843', 'vk6.37308', 'vk6.44076', 'vk6.44417', 'vk6.48505', 'vk6.48586', 'vk6.49193', 'vk6.49303', 'vk6.50288', 'vk6.50362', 'vk6.51055', 'vk6.51088', 'vk6.56048', 'vk6.56324', 'vk6.60605', 'vk6.60950', 'vk6.65714', 'vk6.66010', 'vk6.68755', 'vk6.68965', 'vk6.83503', 'vk6.83826', 'vk6.83982', 'vk6.85385', 'vk6.86314', 'vk6.87089', 'vk6.88340', 'vk6.88969'] |
| 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 | O1O2O3O4U1O5U4U5O6U2U3U6 |
| R3 orbit | {'O1O2O3O4U1O5U4U5O6U2U3U6', 'O1O2O3O4U5U3O6U4U1U2O5U6'} |
| R3 orbit length | 2 |
| Gauss code of -K | O1O2O3O4U5U2U3O5U6U1O6U4 |
| Gauss code of K* | O1O2O3U4U1U2U5O4U6O5O6U3 |
| Gauss code of -K* | O1O2O3U1O4O5U4O6U5U2U3U6 |
| Diagrammatic symmetry type | c |
| Flat genus of the diagram | 2 |
| If K is checkerboard colorable | False |
| If K is almost classical | False |
| Based matrix from Gauss code | [[ 0 -3 -1 1 0 1 2],[ 3 0 2 3 1 1 2],[ 1 -2 0 1 -1 1 2],[-1 -3 -1 0 -1 1 1],[ 0 -1 1 1 0 1 0],[-1 -1 -1 -1 -1 0 0],[-2 -2 -2 -1 0 0 0]] |
| Primitive based matrix | [[ 0 2 1 1 0 -1 -3],[-2 0 0 -1 0 -2 -2],[-1 0 0 -1 -1 -1 -1],[-1 1 1 0 -1 -1 -3],[ 0 0 1 1 0 1 -1],[ 1 2 1 1 -1 0 -2],[ 3 2 1 3 1 2 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,-1,0,1,3,0,1,0,2,2,1,1,1,1,1,1,3,-1,1,2] |
| Phi over symmetry | [-3,-1,0,1,1,2,0,2,1,3,3,2,1,1,1,0,0,2,-1,0,1] |
| Phi of -K | [-3,-1,0,1,1,2,0,2,1,3,3,2,1,1,1,0,0,2,-1,0,1] |
| Phi of K* | [-2,-1,-1,0,1,3,0,1,2,1,3,1,0,1,1,0,1,3,2,2,0] |
| Phi of -K* | [-3,-1,0,1,1,2,2,1,1,3,2,-1,1,1,2,1,1,0,-1,0,1] |
| Symmetry type of based matrix | c |
| u-polynomial | t^3-t^2-t |
| Normalized Jones-Krushkal polynomial | 5z+11 |
| Enhanced Jones-Krushkal polynomial | -8w^3z+13w^2z+11w |
| Inner characteristic polynomial | t^6+30t^4+47t^2 |
| Outer characteristic polynomial | t^7+46t^5+104t^3 |
| Flat arrow polynomial | 4*K1**3 - 2*K1**2 - 2*K1*K2 - 2*K1 + K2 + 2 |
| 2-strand cable arrow polynomial | 128*K1**4*K2**3 - 320*K1**4*K2**2 + 352*K1**4*K2 - 416*K1**4 + 32*K1**3*K2*K3 - 640*K1**2*K2**4 + 896*K1**2*K2**3 - 2272*K1**2*K2**2 + 1960*K1**2*K2 - 1160*K1**2 + 544*K1*K2**3*K3 + 1272*K1*K2*K3 + 8*K1*K3*K4 - 32*K2**6 + 32*K2**4*K4 - 520*K2**4 - 160*K2**2*K3**2 - 8*K2**2*K4**2 + 80*K2**2*K4 - 352*K2**2 + 16*K2*K3*K5 - 240*K3**2 - 14*K4**2 + 812 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{5, 6}, {2, 4}, {1, 3}], [{5, 6}, {2, 4}, {3}, {1}]] |
| If K is slice | False |