| Min(phi) over symmetries of the knot is: [-2,-1,-1,1,1,2,-1,0,1,1,2,0,0,1,1,1,1,2,1,1,-1] |
| Flat knots (up to 7 crossings) with same phi are :['6.908'] |
| Arrow polynomial of the knot is: 4*K1**3 - 4*K1*K2 - K1 + K3 + 1 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.395', '6.430', '6.440', '6.548', '6.551', '6.774', '6.832', '6.887', '6.908', '6.911', '6.1205', '6.1332', '6.1339', '6.1341', '6.1346', '6.1382', '6.1488', '6.1651', '6.1655', '6.1686'] |
| Outer characteristic polynomial of the knot is: t^7+46t^5+65t^3 |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.908'] |
| 2-strand cable arrow polynomial of the knot is: -192*K1**2*K2**4 + 128*K1**2*K2**3 - 912*K1**2*K2**2 + 480*K1**2*K2 - 336*K1**2 + 288*K1*K2**3*K3 + 840*K1*K2*K3 + 72*K1*K3*K4 - 32*K2**6 + 64*K2**4*K4 - 352*K2**4 - 144*K2**2*K3**2 - 48*K2**2*K4**2 + 240*K2**2*K4 - 142*K2**2 + 24*K2*K3*K5 + 16*K2*K4*K6 - 248*K3**2 - 100*K4**2 - 2*K6**2 + 354 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.908'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.16793', 'vk6.16797', 'vk6.16824', 'vk6.16828', 'vk6.17539', 'vk6.17547', 'vk6.17594', 'vk6.17602', 'vk6.18161', 'vk6.18496', 'vk6.18498', 'vk6.23209', 'vk6.23213', 'vk6.24047', 'vk6.24057', 'vk6.24149', 'vk6.24618', 'vk6.25032', 'vk6.35227', 'vk6.35927', 'vk6.36327', 'vk6.36339', 'vk6.36757', 'vk6.37178', 'vk6.37180', 'vk6.39375', 'vk6.41560', 'vk6.42712', 'vk6.43452', 'vk6.43460', 'vk6.43504', 'vk6.44337', 'vk6.45947', 'vk6.47629', 'vk6.54985', 'vk6.55019', 'vk6.55629', 'vk6.55637', 'vk6.55660', 'vk6.55961', 'vk6.59378', 'vk6.59382', 'vk6.60147', 'vk6.62056', 'vk6.65191', 'vk6.65334', 'vk6.68175', 'vk6.68504'] |
| 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 | O1O2O3O4U2U5O6O5U3U4U1U6 |
| R3 orbit | {'O1O2O3U1O4U5O6O5U3U2U4U6', 'O1O2O3U1U4O5O4O6U3U2U6U5', 'O1O2O3O4U2U5O6O5U3U4U1U6'} |
| R3 orbit length | 3 |
| Gauss code of -K | O1O2O3O4U5U4U1U2O6O5U6U3 |
| Gauss code of K* | O1O2O3O4U3U5U1U2O5O6U4U6 |
| Gauss code of -K* | O1O2O3O4U5U1O5O6U3U4U6U2 |
| 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 -1 -2 -1 1 1 2],[ 1 0 -2 0 2 1 2],[ 2 2 0 1 2 2 2],[ 1 0 -1 0 1 1 1],[-1 -2 -2 -1 0 -1 0],[-1 -1 -2 -1 1 0 2],[-2 -2 -2 -1 0 -2 0]] |
| Primitive based matrix | [[ 0 2 1 1 -1 -1 -2],[-2 0 0 -2 -1 -2 -2],[-1 0 0 -1 -1 -2 -2],[-1 2 1 0 -1 -1 -2],[ 1 1 1 1 0 0 -1],[ 1 2 2 1 0 0 -2],[ 2 2 2 2 1 2 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,-1,1,1,2,0,2,1,2,2,1,1,2,2,1,1,2,0,1,2] |
| Phi over symmetry | [-2,-1,-1,1,1,2,-1,0,1,1,2,0,0,1,1,1,1,2,1,1,-1] |
| Phi of -K | [-2,-1,-1,1,1,2,-1,0,1,1,2,0,0,1,1,1,1,2,1,1,-1] |
| Phi of K* | [-2,-1,-1,1,1,2,-1,1,1,2,2,1,1,1,1,0,1,1,0,-1,0] |
| Phi of -K* | [-2,-1,-1,1,1,2,1,2,2,2,2,0,1,1,1,1,2,2,1,2,0] |
| Symmetry type of based matrix | c |
| u-polynomial | 0 |
| Normalized Jones-Krushkal polynomial | z+3 |
| Enhanced Jones-Krushkal polynomial | -8w^3z+9w^2z+3w |
| Inner characteristic polynomial | t^6+34t^4+21t^2 |
| Outer characteristic polynomial | t^7+46t^5+65t^3 |
| Flat arrow polynomial | 4*K1**3 - 4*K1*K2 - K1 + K3 + 1 |
| 2-strand cable arrow polynomial | -192*K1**2*K2**4 + 128*K1**2*K2**3 - 912*K1**2*K2**2 + 480*K1**2*K2 - 336*K1**2 + 288*K1*K2**3*K3 + 840*K1*K2*K3 + 72*K1*K3*K4 - 32*K2**6 + 64*K2**4*K4 - 352*K2**4 - 144*K2**2*K3**2 - 48*K2**2*K4**2 + 240*K2**2*K4 - 142*K2**2 + 24*K2*K3*K5 + 16*K2*K4*K6 - 248*K3**2 - 100*K4**2 - 2*K6**2 + 354 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{2, 6}, {1, 5}, {3, 4}], [{2, 6}, {3, 5}, {1, 4}]] |
| If K is slice | False |