| Min(phi) over symmetries of the knot is: [-2,-1,-1,1,1,2,0,0,1,2,1,-1,0,2,2,1,0,0,-1,1,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.1549'] |
| Arrow polynomial of the knot is: 4*K1**3 - 4*K1**2 - 4*K1*K2 - K1 + 2*K2 + K3 + 3 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.209', '6.231', '6.391', '6.419', '6.600', '6.661', '6.744', '6.812', '6.826', '6.1114', '6.1125', '6.1202', '6.1275', '6.1292', '6.1305', '6.1322', '6.1365', '6.1481', '6.1483', '6.1497', '6.1543', '6.1549', '6.1572', '6.1577', '6.1580', '6.1594', '6.1641', '6.1658', '6.1683', '6.1753', '6.1830', '6.1907', '6.1928'] |
| Outer characteristic polynomial of the knot is: t^7+50t^5+250t^3+13t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1549'] |
| 2-strand cable arrow polynomial of the knot is: -16*K1**4 + 32*K1**3*K2*K3 - 64*K1**3*K3 - 192*K1**2*K2**4 + 192*K1**2*K2**3 + 128*K1**2*K2**2*K4 - 3632*K1**2*K2**2 + 32*K1**2*K2*K3**2 - 192*K1**2*K2*K4 + 4928*K1**2*K2 - 80*K1**2*K3**2 - 80*K1**2*K4**2 - 4120*K1**2 + 320*K1*K2**3*K3 - 704*K1*K2**2*K3 - 192*K1*K2**2*K5 - 32*K1*K2*K3*K4 + 4400*K1*K2*K3 + 520*K1*K3*K4 + 72*K1*K4*K5 - 32*K2**6 + 64*K2**4*K4 - 528*K2**4 - 144*K2**2*K3**2 - 48*K2**2*K4**2 + 1080*K2**2*K4 - 3006*K2**2 + 112*K2*K3*K5 + 16*K2*K4*K6 - 1260*K3**2 - 452*K4**2 - 28*K5**2 - 2*K6**2 + 2906 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1549'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.11064', 'vk6.11144', 'vk6.12230', 'vk6.12339', 'vk6.18334', 'vk6.18671', 'vk6.24772', 'vk6.25229', 'vk6.30643', 'vk6.30738', 'vk6.31875', 'vk6.31946', 'vk6.36958', 'vk6.37418', 'vk6.44149', 'vk6.44470', 'vk6.51855', 'vk6.51900', 'vk6.52720', 'vk6.52825', 'vk6.56120', 'vk6.56343', 'vk6.60639', 'vk6.60978', 'vk6.63514', 'vk6.63560', 'vk6.63996', 'vk6.64042', 'vk6.65775', 'vk6.66035', 'vk6.68780', 'vk6.68989'] |
| 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 | O1O2O3U4O5U2U6O4O6U1U5U3 |
| R3 orbit | {'O1O2O3U4O5U2U6O4O6U1U5U3'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U1U4U3O5O6U5U2O4U6 |
| Gauss code of K* | O1O2O3U1U4U3O5U2O4O6U5U6 |
| Gauss code of -K* | O1O2O3U4U5O4O6U2O5U1U6U3 |
| 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 2 -1 1 1],[ 2 0 1 3 0 1 3],[ 1 -1 0 1 1 0 2],[-2 -3 -1 0 -2 -1 -1],[ 1 0 -1 2 0 2 1],[-1 -1 0 1 -2 0 -1],[-1 -3 -2 1 -1 1 0]] |
| Primitive based matrix | [[ 0 2 1 1 -1 -1 -2],[-2 0 -1 -1 -1 -2 -3],[-1 1 0 1 -2 -1 -3],[-1 1 -1 0 0 -2 -1],[ 1 1 2 0 0 1 -1],[ 1 2 1 2 -1 0 0],[ 2 3 3 1 1 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,-1,1,1,2,1,1,1,2,3,-1,2,1,3,0,2,1,-1,1,0] |
| Phi over symmetry | [-2,-1,-1,1,1,2,0,0,1,2,1,-1,0,2,2,1,0,0,-1,1,0] |
| Phi of -K | [-2,-1,-1,1,1,2,0,1,0,2,1,-1,0,2,2,1,0,1,-1,0,0] |
| Phi of K* | [-2,-1,-1,1,1,2,0,0,1,2,1,-1,0,2,2,1,0,0,-1,1,0] |
| Phi of -K* | [-2,-1,-1,1,1,2,0,1,1,3,3,-1,2,1,2,0,2,1,-1,1,1] |
| Symmetry type of based matrix | c |
| u-polynomial | 0 |
| Normalized Jones-Krushkal polynomial | 6z^2+23z+23 |
| Enhanced Jones-Krushkal polynomial | 6w^3z^2+23w^2z+23w |
| Inner characteristic polynomial | t^6+38t^4+182t^2+9 |
| Outer characteristic polynomial | t^7+50t^5+250t^3+13t |
| Flat arrow polynomial | 4*K1**3 - 4*K1**2 - 4*K1*K2 - K1 + 2*K2 + K3 + 3 |
| 2-strand cable arrow polynomial | -16*K1**4 + 32*K1**3*K2*K3 - 64*K1**3*K3 - 192*K1**2*K2**4 + 192*K1**2*K2**3 + 128*K1**2*K2**2*K4 - 3632*K1**2*K2**2 + 32*K1**2*K2*K3**2 - 192*K1**2*K2*K4 + 4928*K1**2*K2 - 80*K1**2*K3**2 - 80*K1**2*K4**2 - 4120*K1**2 + 320*K1*K2**3*K3 - 704*K1*K2**2*K3 - 192*K1*K2**2*K5 - 32*K1*K2*K3*K4 + 4400*K1*K2*K3 + 520*K1*K3*K4 + 72*K1*K4*K5 - 32*K2**6 + 64*K2**4*K4 - 528*K2**4 - 144*K2**2*K3**2 - 48*K2**2*K4**2 + 1080*K2**2*K4 - 3006*K2**2 + 112*K2*K3*K5 + 16*K2*K4*K6 - 1260*K3**2 - 452*K4**2 - 28*K5**2 - 2*K6**2 + 2906 |
| Genus of based matrix | 0 |
| Fillings of based matrix | [[{4, 6}, {2, 5}, {1, 3}]] |
| If K is slice | True |