| Min(phi) over symmetries of the knot is: [-2,-1,0,0,1,2,-1,0,1,1,2,0,0,1,1,0,1,1,1,2,-1] |
| Flat knots (up to 7 crossings) with same phi are :['6.911'] |
| 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+39t^5+59t^3+5t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.911'] |
| 2-strand cable arrow polynomial of the knot is: 1248*K1**4*K2 - 2528*K1**4 + 672*K1**3*K2*K3 - 960*K1**3*K3 - 128*K1**2*K2**4 + 416*K1**2*K2**3 + 128*K1**2*K2**2*K4 - 3472*K1**2*K2**2 - 704*K1**2*K2*K4 + 4664*K1**2*K2 - 928*K1**2*K3**2 - 32*K1**2*K4**2 - 1984*K1**2 + 288*K1*K2**3*K3 - 544*K1*K2**2*K3 - 160*K1*K2**2*K5 - 256*K1*K2*K3*K4 + 4120*K1*K2*K3 + 1152*K1*K3*K4 + 120*K1*K4*K5 - 32*K2**6 + 64*K2**4*K4 - 640*K2**4 - 272*K2**2*K3**2 - 48*K2**2*K4**2 + 928*K2**2*K4 - 1886*K2**2 + 368*K2*K3*K5 + 16*K2*K4*K6 - 1100*K3**2 - 468*K4**2 - 108*K5**2 - 2*K6**2 + 2066 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.911'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.16809', 'vk6.16813', 'vk6.16864', 'vk6.16868', 'vk6.18175', 'vk6.18177', 'vk6.18512', 'vk6.18514', 'vk6.23249', 'vk6.23253', 'vk6.24634', 'vk6.25057', 'vk6.25059', 'vk6.35242', 'vk6.35270', 'vk6.36769', 'vk6.37207', 'vk6.37209', 'vk6.42764', 'vk6.42768', 'vk6.44351', 'vk6.44353', 'vk6.55004', 'vk6.55034', 'vk6.55972', 'vk6.55974', 'vk6.59407', 'vk6.59411', 'vk6.60508', 'vk6.65636', 'vk6.68190', 'vk6.68194'] |
| 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 | O1O2O3O4U2U5O6O5U4U3U1U6 |
| R3 orbit | {'O1O2O3O4U2U5O6O5U4U3U1U6'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U5U4U2U1O6O5U6U3 |
| Gauss code of K* | O1O2O3O4U3U5U2U1O5O6U4U6 |
| Gauss code of -K* | O1O2O3O4U5U1O5O6U4U3U6U2 |
| 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 -1 -2 0 0 1 2],[ 1 0 -2 1 1 1 2],[ 2 2 0 2 1 2 2],[ 0 -1 -2 0 0 0 1],[ 0 -1 -1 0 0 0 0],[-1 -1 -2 0 0 0 2],[-2 -2 -2 -1 0 -2 0]] |
| Primitive based matrix | [[ 0 2 1 0 0 -1 -2],[-2 0 -2 0 -1 -2 -2],[-1 2 0 0 0 -1 -2],[ 0 0 0 0 0 -1 -1],[ 0 1 0 0 0 -1 -2],[ 1 2 1 1 1 0 -2],[ 2 2 2 1 2 2 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,0,0,1,2,2,0,1,2,2,0,0,1,2,0,1,1,1,2,2] |
| Phi over symmetry | [-2,-1,0,0,1,2,-1,0,1,1,2,0,0,1,1,0,1,1,1,2,-1] |
| Phi of -K | [-2,-1,0,0,1,2,-1,0,1,1,2,0,0,1,1,0,1,1,1,2,-1] |
| Phi of K* | [-2,-1,0,0,1,2,-1,1,2,1,2,1,1,1,1,0,0,0,0,1,-1] |
| Phi of -K* | [-2,-1,0,0,1,2,2,1,2,2,2,1,1,1,2,0,0,0,0,1,2] |
| Symmetry type of based matrix | c |
| u-polynomial | 0 |
| Normalized Jones-Krushkal polynomial | 7z^2+24z+21 |
| Enhanced Jones-Krushkal polynomial | 7w^3z^2+24w^2z+21w |
| Inner characteristic polynomial | t^6+29t^4+21t^2+1 |
| Outer characteristic polynomial | t^7+39t^5+59t^3+5t |
| Flat arrow polynomial | 4*K1**3 - 4*K1*K2 - K1 + K3 + 1 |
| 2-strand cable arrow polynomial | 1248*K1**4*K2 - 2528*K1**4 + 672*K1**3*K2*K3 - 960*K1**3*K3 - 128*K1**2*K2**4 + 416*K1**2*K2**3 + 128*K1**2*K2**2*K4 - 3472*K1**2*K2**2 - 704*K1**2*K2*K4 + 4664*K1**2*K2 - 928*K1**2*K3**2 - 32*K1**2*K4**2 - 1984*K1**2 + 288*K1*K2**3*K3 - 544*K1*K2**2*K3 - 160*K1*K2**2*K5 - 256*K1*K2*K3*K4 + 4120*K1*K2*K3 + 1152*K1*K3*K4 + 120*K1*K4*K5 - 32*K2**6 + 64*K2**4*K4 - 640*K2**4 - 272*K2**2*K3**2 - 48*K2**2*K4**2 + 928*K2**2*K4 - 1886*K2**2 + 368*K2*K3*K5 + 16*K2*K4*K6 - 1100*K3**2 - 468*K4**2 - 108*K5**2 - 2*K6**2 + 2066 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{2, 6}, {1, 5}, {3, 4}], [{2, 6}, {1, 5}, {4}, {3}]] |
| If K is slice | False |