| Min(phi) over symmetries of the knot is: [-3,-2,1,1,1,2,0,1,1,3,4,0,1,1,2,0,0,0,-1,-1,1] |
| Flat knots (up to 7 crossings) with same phi are :['6.657'] |
| Arrow polynomial of the knot is: -8*K1**2 - 2*K1*K2 + K1 + 4*K2 + K3 + 5 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.377', '6.638', '6.646', '6.647', '6.657', '6.658', '6.662', '6.692', '6.695', '6.714', '6.720', '6.726', '6.730', '6.731', '6.749', '6.756', '6.772', '6.779', '6.781', '6.800', '6.829', '6.1085', '6.1089', '6.1302', '6.1349', '6.1350', '6.1360', '6.1362', '6.1375', '6.1384'] |
| Outer characteristic polynomial of the knot is: t^7+56t^5+71t^3 |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.657'] |
| 2-strand cable arrow polynomial of the knot is: -192*K1**4*K2**2 + 608*K1**4*K2 - 1200*K1**4 + 96*K1**3*K2*K3 + 32*K1**3*K3*K4 + 128*K1**2*K2**3 - 1264*K1**2*K2**2 + 1696*K1**2*K2 - 208*K1**2*K3**2 - 32*K1**2*K4**2 - 648*K1**2 + 1080*K1*K2*K3 + 232*K1*K3*K4 + 32*K1*K4*K5 - 128*K2**4 - 48*K2**2*K3**2 - 8*K2**2*K4**2 + 80*K2**2*K4 - 678*K2**2 + 40*K2*K3*K5 + 8*K2*K4*K6 - 332*K3**2 - 100*K4**2 - 20*K5**2 - 2*K6**2 + 826 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.657'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.13928', 'vk6.13949', 'vk6.14023', 'vk6.14045', 'vk6.14999', 'vk6.15016', 'vk6.15120', 'vk6.15138', 'vk6.16537', 'vk6.16630', 'vk6.17448', 'vk6.17469', 'vk6.17487', 'vk6.23956', 'vk6.23978', 'vk6.23989', 'vk6.24011', 'vk6.24112', 'vk6.25997', 'vk6.26383', 'vk6.33746', 'vk6.33829', 'vk6.34938', 'vk6.35056', 'vk6.36271', 'vk6.36363', 'vk6.37604', 'vk6.37693', 'vk6.43411', 'vk6.44586', 'vk6.53880', 'vk6.54430', 'vk6.54782', 'vk6.54871', 'vk6.55600', 'vk6.56436', 'vk6.56551', 'vk6.60103', 'vk6.60109', 'vk6.60188'] |
| 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 | O1O2O3O4U2O5U1U5O6U4U6U3 |
| R3 orbit | {'O1O2O3O4U2O5U1U5U3O6U4U6', 'O1O2O3O4U2O5U1U5O6U4U6U3'} |
| R3 orbit length | 2 |
| Gauss code of -K | O1O2O3O4U2U5U1O5U6U4O6U3 |
| Gauss code of K* | O1O2O3U4U5U3U1O5U6O4O6U2 |
| Gauss code of -K* | O1O2O3U2O4O5U4O6U3U1U6U5 |
| Diagrammatic symmetry type | c |
| Flat genus of the diagram | 2 |
| If K is checkerboard colorable | False |
| If K is almost classical | False |
| Based matrix from Gauss code | [[ 0 -3 -2 2 1 1 1],[ 3 0 0 4 3 1 1],[ 2 0 0 2 1 0 1],[-2 -4 -2 0 -1 0 1],[-1 -3 -1 1 0 0 1],[-1 -1 0 0 0 0 0],[-1 -1 -1 -1 -1 0 0]] |
| Primitive based matrix | [[ 0 2 1 1 1 -2 -3],[-2 0 1 0 -1 -2 -4],[-1 -1 0 0 -1 -1 -1],[-1 0 0 0 0 0 -1],[-1 1 1 0 0 -1 -3],[ 2 2 1 0 1 0 0],[ 3 4 1 1 3 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,-1,-1,2,3,-1,0,1,2,4,0,1,1,1,0,0,1,1,3,0] |
| Phi over symmetry | [-3,-2,1,1,1,2,0,1,1,3,4,0,1,1,2,0,0,0,-1,-1,1] |
| Phi of -K | [-3,-2,1,1,1,2,1,1,3,3,1,2,2,3,2,-1,0,0,0,2,1] |
| Phi of K* | [-2,-1,-1,-1,2,3,0,1,2,2,1,0,1,2,1,0,3,3,2,3,1] |
| Phi of -K* | [-3,-2,1,1,1,2,0,1,1,3,4,0,1,1,2,0,0,0,-1,-1,1] |
| Symmetry type of based matrix | c |
| u-polynomial | t^3-3t |
| Normalized Jones-Krushkal polynomial | 9z+19 |
| Enhanced Jones-Krushkal polynomial | 9w^2z+19w |
| Inner characteristic polynomial | t^6+36t^4+21t^2 |
| Outer characteristic polynomial | t^7+56t^5+71t^3 |
| Flat arrow polynomial | -8*K1**2 - 2*K1*K2 + K1 + 4*K2 + K3 + 5 |
| 2-strand cable arrow polynomial | -192*K1**4*K2**2 + 608*K1**4*K2 - 1200*K1**4 + 96*K1**3*K2*K3 + 32*K1**3*K3*K4 + 128*K1**2*K2**3 - 1264*K1**2*K2**2 + 1696*K1**2*K2 - 208*K1**2*K3**2 - 32*K1**2*K4**2 - 648*K1**2 + 1080*K1*K2*K3 + 232*K1*K3*K4 + 32*K1*K4*K5 - 128*K2**4 - 48*K2**2*K3**2 - 8*K2**2*K4**2 + 80*K2**2*K4 - 678*K2**2 + 40*K2*K3*K5 + 8*K2*K4*K6 - 332*K3**2 - 100*K4**2 - 20*K5**2 - 2*K6**2 + 826 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{4, 6}, {2, 5}, {1, 3}], [{4, 6}, {2, 5}, {3}, {1}]] |
| If K is slice | False |