| Min(phi) over symmetries of the knot is: [-3,-3,0,1,2,3,0,1,1,3,2,2,1,4,3,1,2,2,-1,0,1] |
| Flat knots (up to 7 crossings) with same phi are :['6.303'] |
| 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+88t^5+106t^3+9t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.303'] |
| 2-strand cable arrow polynomial of the knot is: -192*K1**2*K2**4 + 896*K1**2*K2**3 + 128*K1**2*K2**2*K4 - 5072*K1**2*K2**2 - 512*K1**2*K2*K4 + 5280*K1**2*K2 - 64*K1**2*K4**2 - 4112*K1**2 + 352*K1*K2**3*K3 - 768*K1*K2**2*K3 - 96*K1*K2**2*K5 + 5408*K1*K2*K3 + 440*K1*K3*K4 + 24*K1*K4*K5 - 32*K2**6 + 32*K2**4*K4 - 1752*K2**4 - 816*K2**2*K3**2 - 72*K2**2*K4**2 + 1600*K2**2*K4 - 2368*K2**2 + 480*K2*K3*K5 + 64*K2*K4*K6 - 1320*K3**2 - 382*K4**2 - 56*K5**2 - 16*K6**2 + 2924 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.303'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.16998', 'vk6.17239', 'vk6.20531', 'vk6.21931', 'vk6.23403', 'vk6.23710', 'vk6.27987', 'vk6.29454', 'vk6.35470', 'vk6.35915', 'vk6.39387', 'vk6.41578', 'vk6.42904', 'vk6.43203', 'vk6.45964', 'vk6.47641', 'vk6.55173', 'vk6.55417', 'vk6.57395', 'vk6.58570', 'vk6.59553', 'vk6.59891', 'vk6.62062', 'vk6.63049', 'vk6.64977', 'vk6.65185', 'vk6.66939', 'vk6.67796', 'vk6.68267', 'vk6.68421', 'vk6.69549', 'vk6.70249'] |
| 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 | O1O2O3O4O5U2U1O6U4U6U5U3 |
| R3 orbit | {'O1O2O3O4O5U2U1O6U4U6U5U3'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4O5U3U1U6U2O6U5U4 |
| Gauss code of K* | O1O2O3O4U5U6U4U1U3O6O5U2 |
| Gauss code of -K* | O1O2O3O4U3O5O6U2U4U1U6U5 |
| 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 -3 2 0 3 1],[ 3 0 0 4 2 3 1],[ 3 0 0 3 1 2 1],[-2 -4 -3 0 -2 1 1],[ 0 -2 -1 2 0 2 1],[-3 -3 -2 -1 -2 0 0],[-1 -1 -1 -1 -1 0 0]] |
| Primitive based matrix | [[ 0 3 2 1 0 -3 -3],[-3 0 -1 0 -2 -2 -3],[-2 1 0 1 -2 -3 -4],[-1 0 -1 0 -1 -1 -1],[ 0 2 2 1 0 -1 -2],[ 3 2 3 1 1 0 0],[ 3 3 4 1 2 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-3,-2,-1,0,3,3,1,0,2,2,3,-1,2,3,4,1,1,1,1,2,0] |
| Phi over symmetry | [-3,-3,0,1,2,3,0,1,1,3,2,2,1,4,3,1,2,2,-1,0,1] |
| Phi of -K | [-3,-3,0,1,2,3,0,1,3,1,3,2,3,2,4,0,0,1,2,2,0] |
| Phi of K* | [-3,-2,-1,0,3,3,0,2,1,3,4,2,0,1,2,0,3,3,1,2,0] |
| Phi of -K* | [-3,-3,0,1,2,3,0,1,1,3,2,2,1,4,3,1,2,2,-1,0,1] |
| Symmetry type of based matrix | c |
| u-polynomial | t^3-t^2-t |
| Normalized Jones-Krushkal polynomial | 8z^2+25z+19 |
| Enhanced Jones-Krushkal polynomial | -2w^4z^2+10w^3z^2-2w^3z+27w^2z+19w |
| Inner characteristic polynomial | t^6+56t^4+17t^2+1 |
| Outer characteristic polynomial | t^7+88t^5+106t^3+9t |
| Flat arrow polynomial | 4*K1**3 - 2*K1**2 - 2*K1*K2 - 2*K1 + K2 + 2 |
| 2-strand cable arrow polynomial | -192*K1**2*K2**4 + 896*K1**2*K2**3 + 128*K1**2*K2**2*K4 - 5072*K1**2*K2**2 - 512*K1**2*K2*K4 + 5280*K1**2*K2 - 64*K1**2*K4**2 - 4112*K1**2 + 352*K1*K2**3*K3 - 768*K1*K2**2*K3 - 96*K1*K2**2*K5 + 5408*K1*K2*K3 + 440*K1*K3*K4 + 24*K1*K4*K5 - 32*K2**6 + 32*K2**4*K4 - 1752*K2**4 - 816*K2**2*K3**2 - 72*K2**2*K4**2 + 1600*K2**2*K4 - 2368*K2**2 + 480*K2*K3*K5 + 64*K2*K4*K6 - 1320*K3**2 - 382*K4**2 - 56*K5**2 - 16*K6**2 + 2924 |
| 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 |