| Min(phi) over symmetries of the knot is: [-4,-3,1,2,2,2,0,4,2,3,4,3,1,2,3,1,1,1,0,0,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.98'] |
| 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+99t^5+63t^3 |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.98'] |
| 2-strand cable arrow polynomial of the knot is: -144*K1**4 + 192*K1**3*K2*K3 - 288*K1**2*K2**2 + 152*K1**2*K2 - 208*K1**2*K3**2 - 128*K1**2 + 400*K1*K2*K3 + 168*K1*K3*K4 + 48*K1*K4*K5 + 24*K1*K5*K6 - 8*K2**2*K4**2 + 112*K2**2*K4 - 16*K2**2*K5**2 - 8*K2**2*K6**2 - 354*K2**2 + 168*K2*K3*K5 + 48*K2*K4*K6 + 16*K2*K5*K7 + 8*K2*K6*K8 + 24*K3**2*K6 - 284*K3**2 - 154*K4**2 - 120*K5**2 - 46*K6**2 - 4*K7**2 - 2*K8**2 + 402 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.98'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.17119', 'vk6.17360', 'vk6.20098', 'vk6.20263', 'vk6.21201', 'vk6.21576', 'vk6.23515', 'vk6.26933', 'vk6.27167', 'vk6.27519', 'vk6.28685', 'vk6.29099', 'vk6.35668', 'vk6.38351', 'vk6.38577', 'vk6.38922', 'vk6.40493', 'vk6.41134', 'vk6.43023', 'vk6.45214', 'vk6.45464', 'vk6.45673', 'vk6.47037', 'vk6.47398', 'vk6.55264', 'vk6.56748', 'vk6.56915', 'vk6.57853', 'vk6.59673', 'vk6.61197', 'vk6.61450', 'vk6.62429', 'vk6.65069', 'vk6.66454', 'vk6.66619', 'vk6.67227', 'vk6.68327', 'vk6.69100', 'vk6.69263', 'vk6.69879'] |
| 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 | O1O2O3O4O5O6U2U6U1U5U4U3 |
| R3 orbit | {'O1O2O3O4O5O6U2U6U1U5U4U3', 'O1O2O3O4O5U1O6U2U6U5U4U3'} |
| R3 orbit length | 2 |
| Gauss code of -K | O1O2O3O4O5O6U4U3U2U6U1U5 |
| Gauss code of K* | O1O2O3O4O5O6U3U1U6U5U4U2 |
| Gauss code of -K* | O1O2O3O4O5O6U5U3U2U1U6U4 |
| 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 -4 2 2 2 1],[ 3 0 -1 4 3 2 1],[ 4 1 0 4 3 2 1],[-2 -4 -4 0 0 0 0],[-2 -3 -3 0 0 0 0],[-2 -2 -2 0 0 0 0],[-1 -1 -1 0 0 0 0]] |
| Primitive based matrix | [[ 0 2 2 2 1 -3 -4],[-2 0 0 0 0 -2 -2],[-2 0 0 0 0 -3 -3],[-2 0 0 0 0 -4 -4],[-1 0 0 0 0 -1 -1],[ 3 2 3 4 1 0 -1],[ 4 2 3 4 1 1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-2,-2,-1,3,4,0,0,0,2,2,0,0,3,3,0,4,4,1,1,1] |
| Phi over symmetry | [-4,-3,1,2,2,2,0,4,2,3,4,3,1,2,3,1,1,1,0,0,0] |
| Phi of -K | [-4,-3,1,2,2,2,0,4,2,3,4,3,1,2,3,1,1,1,0,0,0] |
| Phi of K* | [-2,-2,-2,-1,3,4,0,0,1,1,2,0,1,2,3,1,3,4,3,4,0] |
| Phi of -K* | [-4,-3,1,2,2,2,1,1,2,3,4,1,2,3,4,0,0,0,0,0,0] |
| Symmetry type of based matrix | c |
| u-polynomial | t^4+t^3-3t^2-t |
| Normalized Jones-Krushkal polynomial | 3z+7 |
| Enhanced Jones-Krushkal polynomial | -6w^3z+9w^2z+7w |
| Inner characteristic polynomial | t^6+61t^4 |
| Outer characteristic polynomial | t^7+99t^5+63t^3 |
| Flat arrow polynomial | -2*K1*K2 - 2*K1*K3 + K1 + K2 + K3 + K4 + 1 |
| 2-strand cable arrow polynomial | -144*K1**4 + 192*K1**3*K2*K3 - 288*K1**2*K2**2 + 152*K1**2*K2 - 208*K1**2*K3**2 - 128*K1**2 + 400*K1*K2*K3 + 168*K1*K3*K4 + 48*K1*K4*K5 + 24*K1*K5*K6 - 8*K2**2*K4**2 + 112*K2**2*K4 - 16*K2**2*K5**2 - 8*K2**2*K6**2 - 354*K2**2 + 168*K2*K3*K5 + 48*K2*K4*K6 + 16*K2*K5*K7 + 8*K2*K6*K8 + 24*K3**2*K6 - 284*K3**2 - 154*K4**2 - 120*K5**2 - 46*K6**2 - 4*K7**2 - 2*K8**2 + 402 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {2, 5}, {3, 4}], [{2, 6}, {3, 5}, {1, 4}], [{2, 6}, {3, 5}, {4}, {1}]] |
| If K is slice | False |