| Min(phi) over symmetries of the knot is: [-2,0,0,0,1,1,0,1,1,1,1,-1,-1,0,1,0,0,0,1,1,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.1835'] |
| 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+25t^5+60t^3+11t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1835'] |
| 2-strand cable arrow polynomial of the knot is: -256*K1**6 + 1376*K1**4*K2 - 4240*K1**4 + 384*K1**3*K2*K3 - 1728*K1**3*K3 + 512*K1**2*K2**3 - 4640*K1**2*K2**2 + 32*K1**2*K2*K3**2 - 576*K1**2*K2*K4 + 11712*K1**2*K2 - 560*K1**2*K3**2 - 64*K1**2*K4**2 - 7724*K1**2 + 128*K1*K2**3*K3 - 928*K1*K2**2*K3 - 32*K1*K2**2*K5 - 160*K1*K2*K3*K4 + 8208*K1*K2*K3 + 1256*K1*K3*K4 + 120*K1*K4*K5 - 552*K2**4 - 208*K2**2*K3**2 - 48*K2**2*K4**2 + 1032*K2**2*K4 - 5868*K2**2 + 192*K2*K3*K5 + 32*K2*K4*K6 - 2744*K3**2 - 598*K4**2 - 60*K5**2 - 4*K6**2 + 6004 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1835'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.4771', 'vk6.4793', 'vk6.5108', 'vk6.5130', 'vk6.6341', 'vk6.6770', 'vk6.6788', 'vk6.8290', 'vk6.8320', 'vk6.8743', 'vk6.9664', 'vk6.9690', 'vk6.9975', 'vk6.10001', 'vk6.21013', 'vk6.21018', 'vk6.22437', 'vk6.22440', 'vk6.28468', 'vk6.40233', 'vk6.40246', 'vk6.42163', 'vk6.46735', 'vk6.46748', 'vk6.48810', 'vk6.49028', 'vk6.49034', 'vk6.49848', 'vk6.49850', 'vk6.51506', 'vk6.58961', 'vk6.69795'] |
| 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 | O1O2O3U1U4O5U6O4O6U3U5U2 |
| R3 orbit | {'O1O2O3U1U4O5U6O4O6U3U5U2'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U2U4U1O5O6U5O4U6U3 |
| Gauss code of K* | O1O2O3U4U3U1O4O5U2O6U5U6 |
| Gauss code of -K* | O1O2O3U4U5O4U2O5O6U3U1U6 |
| 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 -2 1 0 0 0 1],[ 2 0 2 1 2 1 2],[-1 -2 0 -1 -1 0 0],[ 0 -1 1 0 -1 0 1],[ 0 -2 1 1 0 1 0],[ 0 -1 0 0 -1 0 0],[-1 -2 0 -1 0 0 0]] |
| Primitive based matrix | [[ 0 1 1 0 0 0 -2],[-1 0 0 0 0 -1 -2],[-1 0 0 0 -1 -1 -2],[ 0 0 0 0 -1 0 -1],[ 0 0 1 1 0 1 -2],[ 0 1 1 0 -1 0 -1],[ 2 2 2 1 2 1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-1,-1,0,0,0,2,0,0,0,1,2,0,1,1,2,1,0,1,-1,2,1] |
| Phi over symmetry | [-2,0,0,0,1,1,0,1,1,1,1,-1,-1,0,1,0,0,0,1,1,0] |
| Phi of -K | [-2,0,0,0,1,1,0,1,1,1,1,-1,-1,0,1,0,0,0,1,1,0] |
| Phi of K* | [-1,-1,0,0,0,2,0,0,0,1,1,0,1,1,1,-1,0,1,1,0,1] |
| Phi of -K* | [-2,0,0,0,1,1,1,1,2,2,2,0,-1,0,0,-1,1,1,0,1,0] |
| Symmetry type of based matrix | c |
| u-polynomial | t^2-2t |
| Normalized Jones-Krushkal polynomial | 21z+43 |
| Enhanced Jones-Krushkal polynomial | 21w^2z+43w |
| Inner characteristic polynomial | t^6+19t^4+39t^2+1 |
| Outer characteristic polynomial | t^7+25t^5+60t^3+11t |
| Flat arrow polynomial | -10*K1**2 - 4*K1*K2 + 2*K1 + 5*K2 + 2*K3 + 6 |
| 2-strand cable arrow polynomial | -256*K1**6 + 1376*K1**4*K2 - 4240*K1**4 + 384*K1**3*K2*K3 - 1728*K1**3*K3 + 512*K1**2*K2**3 - 4640*K1**2*K2**2 + 32*K1**2*K2*K3**2 - 576*K1**2*K2*K4 + 11712*K1**2*K2 - 560*K1**2*K3**2 - 64*K1**2*K4**2 - 7724*K1**2 + 128*K1*K2**3*K3 - 928*K1*K2**2*K3 - 32*K1*K2**2*K5 - 160*K1*K2*K3*K4 + 8208*K1*K2*K3 + 1256*K1*K3*K4 + 120*K1*K4*K5 - 552*K2**4 - 208*K2**2*K3**2 - 48*K2**2*K4**2 + 1032*K2**2*K4 - 5868*K2**2 + 192*K2*K3*K5 + 32*K2*K4*K6 - 2744*K3**2 - 598*K4**2 - 60*K5**2 - 4*K6**2 + 6004 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{3, 6}, {1, 5}, {2, 4}]] |
| If K is slice | False |