| Min(phi) over symmetries of the knot is: [-4,-2,1,1,1,3,1,1,2,3,4,0,1,2,2,0,0,-1,0,0,1] |
| Flat knots (up to 7 crossings) with same phi are :['6.154'] |
| 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+108t^5+74t^3 |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.154'] |
| 2-strand cable arrow polynomial of the knot is: 48*K1**2*K2 - 416*K1**2*K3**2 - 508*K1**2 + 1016*K1*K2*K3 + 488*K1*K3*K4 + 32*K1*K4*K5 + 8*K1*K5*K6 + 8*K1*K6*K7 - 432*K2**2*K3**2 - 8*K2**2*K4**2 + 112*K2**2*K4 - 8*K2**2*K6**2 - 498*K2**2 + 336*K2*K3*K5 + 16*K2*K4*K6 + 8*K2*K5*K7 + 8*K2*K6*K8 - 496*K3**2 - 214*K4**2 - 84*K5**2 - 14*K6**2 - 8*K7**2 - 2*K8**2 + 606 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.154'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.16931', 'vk6.17172', 'vk6.20225', 'vk6.21519', 'vk6.23327', 'vk6.23620', 'vk6.27427', 'vk6.29037', 'vk6.35365', 'vk6.35786', 'vk6.38840', 'vk6.41032', 'vk6.42842', 'vk6.43120', 'vk6.45601', 'vk6.47360', 'vk6.55085', 'vk6.55335', 'vk6.57058', 'vk6.58182', 'vk6.59480', 'vk6.59769', 'vk6.61575', 'vk6.62747', 'vk6.64927', 'vk6.65133', 'vk6.66676', 'vk6.67514', 'vk6.68222', 'vk6.68363', 'vk6.69329', 'vk6.70080', 'vk6.81989', 'vk6.82722', 'vk6.84832', 'vk6.86230', 'vk6.88490', 'vk6.88645', 'vk6.89652', 'vk6.89654'] |
| 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 | O1O2O3O4O5U1O6U3U5U4U6U2 |
| R3 orbit | {'O1O2O3O4O5U1O6U3U5U4U6U2', 'O1O2O3O4O5U1U2O6U5U4U3U6'} |
| R3 orbit length | 2 |
| Gauss code of -K | O1O2O3O4O5U4U6U2U1U3O6U5 |
| Gauss code of K* | O1O2O3O4O5U6U5U1U3U2O6U4 |
| Gauss code of -K* | O1O2O3O4O5U2O6U4U3U5U1U6 |
| 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 1 -2 1 1 3],[ 4 0 4 1 3 2 3],[-1 -4 0 -3 0 0 3],[ 2 -1 3 0 2 1 3],[-1 -3 0 -2 0 0 2],[-1 -2 0 -1 0 0 1],[-3 -3 -3 -3 -2 -1 0]] |
| Primitive based matrix | [[ 0 3 1 1 1 -2 -4],[-3 0 -1 -2 -3 -3 -3],[-1 1 0 0 0 -1 -2],[-1 2 0 0 0 -2 -3],[-1 3 0 0 0 -3 -4],[ 2 3 1 2 3 0 -1],[ 4 3 2 3 4 1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-3,-1,-1,-1,2,4,1,2,3,3,3,0,0,1,2,0,2,3,3,4,1] |
| Phi over symmetry | [-4,-2,1,1,1,3,1,1,2,3,4,0,1,2,2,0,0,-1,0,0,1] |
| Phi of -K | [-4,-2,1,1,1,3,1,1,2,3,4,0,1,2,2,0,0,-1,0,0,1] |
| Phi of K* | [-3,-1,-1,-1,2,4,-1,0,1,2,4,0,0,0,1,0,1,2,2,3,1] |
| Phi of -K* | [-4,-2,1,1,1,3,1,2,3,4,3,1,2,3,3,0,0,1,0,2,3] |
| Symmetry type of based matrix | c |
| u-polynomial | t^4-t^3+t^2-3t |
| Normalized Jones-Krushkal polynomial | 3z+7 |
| Enhanced Jones-Krushkal polynomial | 4w^4z-8w^3z+7w^2z+7w |
| Inner characteristic polynomial | t^6+76t^4+17t^2 |
| Outer characteristic polynomial | t^7+108t^5+74t^3 |
| Flat arrow polynomial | -2*K1*K2 - 2*K1*K3 + K1 + K2 + K3 + K4 + 1 |
| 2-strand cable arrow polynomial | 48*K1**2*K2 - 416*K1**2*K3**2 - 508*K1**2 + 1016*K1*K2*K3 + 488*K1*K3*K4 + 32*K1*K4*K5 + 8*K1*K5*K6 + 8*K1*K6*K7 - 432*K2**2*K3**2 - 8*K2**2*K4**2 + 112*K2**2*K4 - 8*K2**2*K6**2 - 498*K2**2 + 336*K2*K3*K5 + 16*K2*K4*K6 + 8*K2*K5*K7 + 8*K2*K6*K8 - 496*K3**2 - 214*K4**2 - 84*K5**2 - 14*K6**2 - 8*K7**2 - 2*K8**2 + 606 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{5, 6}, {2, 4}, {1, 3}]] |
| If K is slice | False |