| Min(phi) over symmetries of the knot is: [-2,-1,0,1,1,1,0,1,1,1,2,1,0,1,1,1,0,1,0,0,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.1552', '6.1814', '7.30914', '7.33303'] |
| Arrow polynomial of the knot is: -10*K1**2 - 4*K1*K2 + 2*K1 + 5*K2 + 2*K3 + 6 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.425', '6.655', '6.755', '6.769', '6.792', '6.1240', '6.1494', '6.1522', '6.1534', '6.1587', '6.1707', '6.1746', '6.1747', '6.1786', '6.1814', '6.1828', '6.1835', '6.1854', '6.1870'] |
| Outer characteristic polynomial of the knot is: t^7+26t^5+33t^3+4t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1552', '6.1814', '7.33303'] |
| 2-strand cable arrow polynomial of the knot is: -320*K1**4*K2**2 + 1248*K1**4*K2 - 4224*K1**4 + 896*K1**3*K2*K3 - 1280*K1**3*K3 + 128*K1**2*K2**3 - 5072*K1**2*K2**2 - 416*K1**2*K2*K4 + 9808*K1**2*K2 - 1120*K1**2*K3**2 - 5784*K1**2 - 544*K1*K2**2*K3 - 160*K1*K2*K3*K4 + 8312*K1*K2*K3 + 1424*K1*K3*K4 + 80*K1*K4*K5 - 456*K2**4 - 592*K2**2*K3**2 - 112*K2**2*K4**2 + 896*K2**2*K4 - 5012*K2**2 - 96*K2*K3**2*K4 + 528*K2*K3*K5 + 136*K2*K4*K6 + 24*K3**2*K6 - 2724*K3**2 - 622*K4**2 - 116*K5**2 - 28*K6**2 + 5196 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1814'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.4845', 'vk6.4854', 'vk6.5189', 'vk6.5199', 'vk6.6418', 'vk6.6429', 'vk6.6849', 'vk6.8383', 'vk6.8386', 'vk6.8807', 'vk6.8811', 'vk6.9747', 'vk6.9749', 'vk6.10045', 'vk6.20785', 'vk6.20795', 'vk6.22188', 'vk6.29754', 'vk6.39827', 'vk6.39833', 'vk6.46390', 'vk6.46392', 'vk6.47968', 'vk6.47970', 'vk6.49071', 'vk6.49093', 'vk6.49907', 'vk6.51330', 'vk6.51341', 'vk6.51548', 'vk6.58803', 'vk6.63270'] |
| 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 | O1O2O3U4U5O6O5U2U6O4U1U3 |
| R3 orbit | {'O1O2O3U4U5O6O5U2U6O4U1U3'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U1U3O4U5U2O6O5U6U4 |
| Gauss code of K* | O1O2U3O4O5U4U1U5O3O6U2U6 |
| Gauss code of -K* | O1O2U3O4O5U6U4O6O3U1U5U2 |
| 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 -1 2 -1 1 0],[ 1 0 0 2 0 2 0],[ 1 0 0 1 0 1 0],[-2 -2 -1 0 -2 -1 -1],[ 1 0 0 2 0 1 1],[-1 -2 -1 1 -1 0 0],[ 0 0 0 1 -1 0 0]] |
| Primitive based matrix | [[ 0 2 1 0 -1 -1 -1],[-2 0 -1 -1 -1 -2 -2],[-1 1 0 0 -1 -1 -2],[ 0 1 0 0 0 -1 0],[ 1 1 1 0 0 0 0],[ 1 2 1 1 0 0 0],[ 1 2 2 0 0 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,0,1,1,1,1,1,1,2,2,0,1,1,2,0,1,0,0,0,0] |
| Phi over symmetry | [-2,-1,0,1,1,1,0,1,1,1,2,1,0,1,1,1,0,1,0,0,0] |
| Phi of -K | [-1,-1,-1,0,1,2,0,0,0,1,1,0,1,0,1,1,1,2,1,1,0] |
| Phi of K* | [-2,-1,0,1,1,1,0,1,1,1,2,1,0,1,1,1,0,1,0,0,0] |
| Phi of -K* | [-1,-1,-1,0,1,2,0,0,0,1,1,0,0,2,2,1,1,2,0,1,1] |
| Symmetry type of based matrix | c |
| u-polynomial | -t^2+2t |
| Normalized Jones-Krushkal polynomial | 2z^2+23z+39 |
| Enhanced Jones-Krushkal polynomial | 2w^3z^2+23w^2z+39w |
| Inner characteristic polynomial | t^6+18t^4+20t^2 |
| Outer characteristic polynomial | t^7+26t^5+33t^3+4t |
| Flat arrow polynomial | -10*K1**2 - 4*K1*K2 + 2*K1 + 5*K2 + 2*K3 + 6 |
| 2-strand cable arrow polynomial | -320*K1**4*K2**2 + 1248*K1**4*K2 - 4224*K1**4 + 896*K1**3*K2*K3 - 1280*K1**3*K3 + 128*K1**2*K2**3 - 5072*K1**2*K2**2 - 416*K1**2*K2*K4 + 9808*K1**2*K2 - 1120*K1**2*K3**2 - 5784*K1**2 - 544*K1*K2**2*K3 - 160*K1*K2*K3*K4 + 8312*K1*K2*K3 + 1424*K1*K3*K4 + 80*K1*K4*K5 - 456*K2**4 - 592*K2**2*K3**2 - 112*K2**2*K4**2 + 896*K2**2*K4 - 5012*K2**2 - 96*K2*K3**2*K4 + 528*K2*K3*K5 + 136*K2*K4*K6 + 24*K3**2*K6 - 2724*K3**2 - 622*K4**2 - 116*K5**2 - 28*K6**2 + 5196 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{5, 6}, {2, 4}, {1, 3}], [{5, 6}, {3, 4}, {1, 2}], [{6}, {5}, {3, 4}, {1, 2}]] |
| If K is slice | False |