| Min(phi) over symmetries of the knot is: [-4,-3,1,2,2,2,0,1,3,4,5,0,1,2,3,0,0,0,0,0,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.198'] |
| Arrow polynomial of the knot is: -2*K1*K2 - 2*K1*K3 + K1 + K2 + K3 + K4 + 1 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.58', '6.76', '6.78', '6.90', '6.98', '6.154', '6.161', '6.162', '6.198', '6.280', '6.284', '6.345', '6.417', '6.421', '6.435', '6.511'] |
| Outer characteristic polynomial of the knot is: t^7+103t^5+173t^3 |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.198'] |
| 2-strand cable arrow polynomial of the knot is: -144*K1**4 + 96*K1**3*K3*K4 + 168*K1**2*K2 - 752*K1**2*K3**2 - 208*K1**2*K4**2 - 972*K1**2 + 1632*K1*K2*K3 + 1224*K1*K3*K4 + 152*K1*K4*K5 + 8*K1*K5*K6 + 24*K1*K6*K7 - 560*K2**2*K3**2 - 8*K2**2*K4**2 + 160*K2**2*K4 - 8*K2**2*K6**2 - 810*K2**2 + 416*K2*K3*K5 + 48*K2*K4*K6 + 8*K2*K5*K7 + 8*K2*K6*K8 - 64*K3**4 + 96*K3**2*K6 - 996*K3**2 - 530*K4**2 - 112*K5**2 - 70*K6**2 - 16*K7**2 - 2*K8**2 + 1210 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.198'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.17122', 'vk6.17365', 'vk6.20257', 'vk6.21564', 'vk6.23522', 'vk6.23857', 'vk6.27495', 'vk6.29087', 'vk6.35683', 'vk6.36112', 'vk6.38910', 'vk6.41111', 'vk6.43030', 'vk6.43338', 'vk6.45661', 'vk6.47392', 'vk6.55271', 'vk6.55519', 'vk6.57086', 'vk6.58244', 'vk6.59688', 'vk6.60027', 'vk6.61644', 'vk6.62820', 'vk6.65076', 'vk6.65265', 'vk6.66723', 'vk6.67585', 'vk6.68330', 'vk6.68478', 'vk6.69369', 'vk6.70109'] |
| 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 | O1O2O3O4O5U2O6U1U6U5U4U3 |
| R3 orbit | {'O1O2O3O4O5U2O6U1U6U5U4U3'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4O5U3U2U1U6U5O6U4 |
| Gauss code of K* | O1O2O3O4O5U1U6U5U4U3O6U2 |
| Gauss code of -K* | O1O2O3O4O5U4O6U3U2U1U6U5 |
| 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 -4 -3 2 2 2 1],[ 4 0 0 5 4 3 1],[ 3 0 0 3 2 1 0],[-2 -5 -3 0 0 0 0],[-2 -4 -2 0 0 0 0],[-2 -3 -1 0 0 0 0],[-1 -1 0 0 0 0 0]] |
| Primitive based matrix | [[ 0 2 2 2 1 -3 -4],[-2 0 0 0 0 -1 -3],[-2 0 0 0 0 -2 -4],[-2 0 0 0 0 -3 -5],[-1 0 0 0 0 0 -1],[ 3 1 2 3 0 0 0],[ 4 3 4 5 1 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-2,-2,-1,3,4,0,0,0,1,3,0,0,2,4,0,3,5,0,1,0] |
| Phi over symmetry | [-4,-3,1,2,2,2,0,1,3,4,5,0,1,2,3,0,0,0,0,0,0] |
| Phi of -K | [-4,-3,1,2,2,2,1,4,1,2,3,4,2,3,4,1,1,1,0,0,0] |
| Phi of K* | [-2,-2,-2,-1,3,4,0,0,1,2,1,0,1,3,2,1,4,3,4,4,1] |
| Phi of -K* | [-4,-3,1,2,2,2,0,1,3,4,5,0,1,2,3,0,0,0,0,0,0] |
| Symmetry type of based matrix | c |
| u-polynomial | t^4+t^3-3t^2-t |
| Normalized Jones-Krushkal polynomial | 5z+11 |
| Enhanced Jones-Krushkal polynomial | 4w^4z-10w^3z+11w^2z+11w |
| Inner characteristic polynomial | t^6+65t^4+38t^2 |
| Outer characteristic polynomial | t^7+103t^5+173t^3 |
| Flat arrow polynomial | -2*K1*K2 - 2*K1*K3 + K1 + K2 + K3 + K4 + 1 |
| 2-strand cable arrow polynomial | -144*K1**4 + 96*K1**3*K3*K4 + 168*K1**2*K2 - 752*K1**2*K3**2 - 208*K1**2*K4**2 - 972*K1**2 + 1632*K1*K2*K3 + 1224*K1*K3*K4 + 152*K1*K4*K5 + 8*K1*K5*K6 + 24*K1*K6*K7 - 560*K2**2*K3**2 - 8*K2**2*K4**2 + 160*K2**2*K4 - 8*K2**2*K6**2 - 810*K2**2 + 416*K2*K3*K5 + 48*K2*K4*K6 + 8*K2*K5*K7 + 8*K2*K6*K8 - 64*K3**4 + 96*K3**2*K6 - 996*K3**2 - 530*K4**2 - 112*K5**2 - 70*K6**2 - 16*K7**2 - 2*K8**2 + 1210 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{2, 6}, {4, 5}, {1, 3}]] |
| If K is slice | False |