| Min(phi) over symmetries of the knot is: [-3,0,0,0,1,2,1,1,2,3,1,-1,-1,0,1,1,1,1,1,2,2] |
| Flat knots (up to 7 crossings) with same phi are :['6.588'] |
| Arrow polynomial of the knot is: 12*K1**3 - 6*K1**2 - 6*K1*K2 - 6*K1 + 3*K2 + 4 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.212', '6.358', '6.588', '6.589', '6.603', '6.990'] |
| Outer characteristic polynomial of the knot is: t^7+45t^5+77t^3 |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.588'] |
| 2-strand cable arrow polynomial of the knot is: -64*K1**4*K2**2 + 160*K1**4*K2 - 496*K1**4 + 96*K1**3*K2*K3 - 128*K1**2*K2**4 + 352*K1**2*K2**3 - 1888*K1**2*K2**2 + 1968*K1**2*K2 - 48*K1**2*K3**2 - 32*K1**2*K4**2 - 1328*K1**2 + 320*K1*K2**3*K3 + 1632*K1*K2*K3 + 160*K1*K3*K4 + 32*K1*K4*K5 - 224*K2**6 + 160*K2**4*K4 - 1048*K2**4 - 384*K2**2*K3**2 - 72*K2**2*K4**2 + 712*K2**2*K4 - 532*K2**2 + 160*K2*K3*K5 + 32*K2*K4*K6 - 488*K3**2 - 214*K4**2 - 24*K5**2 - 4*K6**2 + 1188 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.588'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.10139', 'vk6.10198', 'vk6.10341', 'vk6.10426', 'vk6.17667', 'vk6.17714', 'vk6.24230', 'vk6.24277', 'vk6.24798', 'vk6.25255', 'vk6.29918', 'vk6.29963', 'vk6.30026', 'vk6.30077', 'vk6.30976', 'vk6.31103', 'vk6.32156', 'vk6.32275', 'vk6.36592', 'vk6.36980', 'vk6.43591', 'vk6.43701', 'vk6.51703', 'vk6.51724', 'vk6.52056', 'vk6.52138', 'vk6.55697', 'vk6.55754', 'vk6.60263', 'vk6.60325', 'vk6.60647', 'vk6.60988', 'vk6.63332', 'vk6.63357', 'vk6.63378', 'vk6.63399', 'vk6.65446', 'vk6.65780', 'vk6.68543', 'vk6.68574'] |
| 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 | O1O2O3O4U1O5U4O6U5U3U6U2 |
| R3 orbit | {'O1O2O3O4U1U3O5O6U4U5U6U2', 'O1O2O3O4U1O5U4O6U5U3U6U2'} |
| R3 orbit length | 2 |
| Gauss code of -K | O1O2O3O4U3U5U2U6O5U1O6U4 |
| Gauss code of K* | O1O2O3O4U5U4U2U6O5U1O6U3 |
| Gauss code of -K* | O1O2O3O4U2O5U4O6U5U3U1U6 |
| 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 1 0 0 0 2],[ 3 0 3 2 1 1 1],[-1 -3 0 -1 -1 0 2],[ 0 -2 1 0 -1 1 2],[ 0 -1 1 1 0 1 1],[ 0 -1 0 -1 -1 0 1],[-2 -1 -2 -2 -1 -1 0]] |
| Primitive based matrix | [[ 0 2 1 0 0 0 -3],[-2 0 -2 -1 -1 -2 -1],[-1 2 0 0 -1 -1 -3],[ 0 1 0 0 -1 -1 -1],[ 0 1 1 1 0 1 -1],[ 0 2 1 1 -1 0 -2],[ 3 1 3 1 1 2 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,0,0,0,3,2,1,1,2,1,0,1,1,3,1,1,1,-1,1,2] |
| Phi over symmetry | [-3,0,0,0,1,2,1,1,2,3,1,-1,-1,0,1,1,1,1,1,2,2] |
| Phi of -K | [-3,0,0,0,1,2,1,2,2,1,4,-1,1,0,0,1,1,1,0,1,-1] |
| Phi of K* | [-2,-1,0,0,0,3,-1,0,1,1,4,0,0,1,1,-1,1,1,1,2,2] |
| Phi of -K* | [-3,0,0,0,1,2,1,1,2,3,1,-1,-1,0,1,1,1,1,1,2,2] |
| Symmetry type of based matrix | c |
| u-polynomial | t^3-t^2-t |
| Normalized Jones-Krushkal polynomial | 7z+15 |
| Enhanced Jones-Krushkal polynomial | -6w^3z+13w^2z+15w |
| Inner characteristic polynomial | t^6+31t^4+20t^2 |
| Outer characteristic polynomial | t^7+45t^5+77t^3 |
| Flat arrow polynomial | 12*K1**3 - 6*K1**2 - 6*K1*K2 - 6*K1 + 3*K2 + 4 |
| 2-strand cable arrow polynomial | -64*K1**4*K2**2 + 160*K1**4*K2 - 496*K1**4 + 96*K1**3*K2*K3 - 128*K1**2*K2**4 + 352*K1**2*K2**3 - 1888*K1**2*K2**2 + 1968*K1**2*K2 - 48*K1**2*K3**2 - 32*K1**2*K4**2 - 1328*K1**2 + 320*K1*K2**3*K3 + 1632*K1*K2*K3 + 160*K1*K3*K4 + 32*K1*K4*K5 - 224*K2**6 + 160*K2**4*K4 - 1048*K2**4 - 384*K2**2*K3**2 - 72*K2**2*K4**2 + 712*K2**2*K4 - 532*K2**2 + 160*K2*K3*K5 + 32*K2*K4*K6 - 488*K3**2 - 214*K4**2 - 24*K5**2 - 4*K6**2 + 1188 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{4, 6}, {1, 5}, {2, 3}]] |
| If K is slice | False |