| Min(phi) over symmetries of the knot is: [-2,-2,1,1,1,1,-1,0,1,2,2,1,1,1,2,0,0,-1,0,0,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.1680'] |
| Arrow polynomial of the knot is: -4*K1**2 - 4*K1*K2 + 2*K1 + 2*K2 + 2*K3 + 3 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.65', '6.137', '6.201', '6.203', '6.214', '6.310', '6.314', '6.332', '6.385', '6.386', '6.401', '6.516', '6.564', '6.571', '6.572', '6.578', '6.621', '6.626', '6.716', '6.773', '6.807', '6.814', '6.821', '6.940', '6.966', '6.1036', '6.1071', '6.1108', '6.1111', '6.1131', '6.1188', '6.1203', '6.1206', '6.1220', '6.1340', '6.1387', '6.1548', '6.1663', '6.1680', '6.1693', '6.1831', '6.1932'] |
| Outer characteristic polynomial of the knot is: t^7+42t^5+62t^3+11t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1680'] |
| 2-strand cable arrow polynomial of the knot is: -2288*K1**4 + 352*K1**3*K2*K3 + 32*K1**3*K3*K4 - 288*K1**3*K3 + 96*K1**2*K2**2*K4 - 3248*K1**2*K2**2 - 992*K1**2*K2*K4 + 5720*K1**2*K2 - 240*K1**2*K3**2 - 128*K1**2*K4**2 - 3056*K1**2 - 672*K1*K2**2*K3 - 224*K1*K2**2*K5 - 32*K1*K2*K3*K4 + 4888*K1*K2*K3 + 1472*K1*K3*K4 + 176*K1*K4*K5 - 432*K2**4 - 80*K2**2*K3**2 - 48*K2**2*K4**2 + 1136*K2**2*K4 - 2844*K2**2 + 192*K2*K3*K5 + 32*K2*K4*K6 - 1596*K3**2 - 752*K4**2 - 84*K5**2 - 4*K6**2 + 2910 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1680'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.13388', 'vk6.13475', 'vk6.13666', 'vk6.13770', 'vk6.14209', 'vk6.14462', 'vk6.15685', 'vk6.16133', 'vk6.16758', 'vk6.16770', 'vk6.16893', 'vk6.19050', 'vk6.19299', 'vk6.19592', 'vk6.23171', 'vk6.23272', 'vk6.25659', 'vk6.26489', 'vk6.33139', 'vk6.33192', 'vk6.33296', 'vk6.35158', 'vk6.35189', 'vk6.37760', 'vk6.42661', 'vk6.42676', 'vk6.42792', 'vk6.44723', 'vk6.53564', 'vk6.53696', 'vk6.54967', 'vk6.64616'] |
| 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 | O1O2O3U2O4U5U6U3O6O5U1U4 |
| R3 orbit | {'O1O2O3U2O4U5U6U3O6O5U1U4'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U4U3O5O6U1U6U5O4U2 |
| Gauss code of K* | O1O2O3U2U1O4O5U4U6U3O6U5 |
| Gauss code of -K* | O1O2O3U4O5U1U5U6O4O6U3U2 |
| 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 2 -1 -1],[ 1 0 -1 3 2 0 0],[ 1 1 0 1 1 0 0],[-2 -3 -1 0 -1 -1 -2],[-2 -2 -1 1 0 -2 -2],[ 1 0 0 1 2 0 0],[ 1 0 0 2 2 0 0]] |
| Primitive based matrix | [[ 0 2 2 -1 -1 -1 -1],[-2 0 1 -1 -2 -2 -2],[-2 -1 0 -1 -1 -2 -3],[ 1 1 1 0 0 0 1],[ 1 2 1 0 0 0 0],[ 1 2 2 0 0 0 0],[ 1 2 3 -1 0 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-2,1,1,1,1,-1,1,2,2,2,1,1,2,3,0,0,-1,0,0,0] |
| Phi over symmetry | [-2,-2,1,1,1,1,-1,0,1,2,2,1,1,1,2,0,0,-1,0,0,0] |
| Phi of -K | [-1,-1,-1,-1,2,2,-1,0,0,2,2,0,0,0,1,0,1,1,2,1,1] |
| Phi of K* | [-2,-2,1,1,1,1,-1,0,1,2,2,1,1,1,2,0,0,-1,0,0,0] |
| Phi of -K* | [-1,-1,-1,-1,2,2,-1,0,0,2,3,0,0,1,1,0,2,1,2,2,1] |
| Symmetry type of based matrix | c |
| u-polynomial | -2t^2+4t |
| Normalized Jones-Krushkal polynomial | 4z^2+17z+19 |
| Enhanced Jones-Krushkal polynomial | -4w^4z^2+8w^3z^2-4w^3z+21w^2z+19w |
| Inner characteristic polynomial | t^6+30t^4+38t^2+4 |
| Outer characteristic polynomial | t^7+42t^5+62t^3+11t |
| Flat arrow polynomial | -4*K1**2 - 4*K1*K2 + 2*K1 + 2*K2 + 2*K3 + 3 |
| 2-strand cable arrow polynomial | -2288*K1**4 + 352*K1**3*K2*K3 + 32*K1**3*K3*K4 - 288*K1**3*K3 + 96*K1**2*K2**2*K4 - 3248*K1**2*K2**2 - 992*K1**2*K2*K4 + 5720*K1**2*K2 - 240*K1**2*K3**2 - 128*K1**2*K4**2 - 3056*K1**2 - 672*K1*K2**2*K3 - 224*K1*K2**2*K5 - 32*K1*K2*K3*K4 + 4888*K1*K2*K3 + 1472*K1*K3*K4 + 176*K1*K4*K5 - 432*K2**4 - 80*K2**2*K3**2 - 48*K2**2*K4**2 + 1136*K2**2*K4 - 2844*K2**2 + 192*K2*K3*K5 + 32*K2*K4*K6 - 1596*K3**2 - 752*K4**2 - 84*K5**2 - 4*K6**2 + 2910 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{2, 6}, {1, 5}, {3, 4}], [{5, 6}, {3, 4}, {1, 2}]] |
| If K is slice | False |