| Min(phi) over symmetries of the knot is: [-4,-1,0,2,3,1,3,2,4,1,1,2,1,2,0] |
| Flat knots (up to 7 crossings) with same phi are :['5.6'] |
| Arrow polynomial of the knot is: 4*K1**2 + 2*K1*K2 + 2*K1*K3 - K1 - 3*K2 - K3 - K4 - 1 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['5.6', '7.1421', '7.1511', '7.1521', '7.2626', '7.2980', '7.2991', '7.3082', '7.3457', '7.3817', '7.4426', '7.4491', '7.4543', '7.5056', '7.5783', '7.5867', '7.6099', '7.6255', '7.6269', '7.6286', '7.6345', '7.6349', '7.7120', '7.7129', '7.7133', '7.7146', '7.7196', '7.7199', '7.7413', '7.7506', '7.8261', '7.8265', '7.8266', '7.8328', '7.9086', '7.9093', '7.9251', '7.9265', '7.9423', '7.9458', '7.9848', '7.10454', '7.10613', '7.10617', '7.11227', '7.11231', '7.11345', '7.11424', '7.11676', '7.13110', '7.13296', '7.14902', '7.14939', '7.15665', '7.15795', '7.15798', '7.16093', '7.17349', '7.17586'] |
| Outer characteristic polynomial of the knot is: t^6+71t^4+15t^2 |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['5.6'] |
| 2-strand cable arrow polynomial of the knot is: -48*K1**2*K2**2 + 272*K1**2*K2 - 160*K1**2*K3**2 - 596*K1**2 + 64*K1*K2*K3**3 + 704*K1*K2*K3 + 176*K1*K3*K4 + 24*K1*K4*K5 + 16*K1*K5*K6 + 8*K1*K6*K7 - 16*K2**4 - 192*K2**2*K3**2 - 8*K2**2*K4**2 + 72*K2**2*K4 - 8*K2**2*K6**2 - 474*K2**2 + 112*K2*K3*K5 + 24*K2*K4*K6 + 8*K2*K5*K7 + 8*K2*K6*K8 - 32*K3**4 - 308*K3**2 - 106*K4**2 - 40*K5**2 - 22*K6**2 - 8*K7**2 - 2*K8**2 + 530 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['5.6'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk5.1974', 'vk5.1990', 'vk5.1992', 'vk5.2037', 'vk5.2043', 'vk5.2075', 'vk5.2092', 'vk5.2096', 'vk5.2112', 'vk5.2116', 'vk5.2149', 'vk5.2153', 'vk5.2279', 'vk5.2281', 'vk5.2310', 'vk5.2402'] |
| 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 | O1O2O3O4O5U1U3U5U2U4 |
| R3 orbit | {'O1O2O3O4O5U1U3U5U2U4'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4O5U2U4U1U3U5 |
| Gauss code of K* | O1O2O3O4O5U1U4U2U5U3 |
| Gauss code of -K* | O1O2O3O4O5U3U1U4U2U5 |
| 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 0 -1 3 2],[ 4 0 3 1 4 2],[ 0 -3 0 -1 2 1],[ 1 -1 1 0 2 1],[-3 -4 -2 -2 0 0],[-2 -2 -1 -1 0 0]] |
| Primitive based matrix | [[ 0 3 2 0 -1 -4],[-3 0 0 -2 -2 -4],[-2 0 0 -1 -1 -2],[ 0 2 1 0 -1 -3],[ 1 2 1 1 0 -1],[ 4 4 2 3 1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-3,-2,0,1,4,0,2,2,4,1,1,2,1,3,1] |
| Phi over symmetry | [-4,-1,0,2,3,1,3,2,4,1,1,2,1,2,0] |
| Phi of -K | [-4,-1,0,2,3,2,1,4,3,0,2,2,1,1,1] |
| Phi of K* | [-3,-2,0,1,4,1,1,2,3,1,2,4,0,1,2] |
| Phi of -K* | [-4,-1,0,2,3,1,3,2,4,1,1,2,1,2,0] |
| Symmetry type of based matrix | c |
| u-polynomial | t^4-t^3-t^2+t |
| Normalized Jones-Krushkal polynomial | -7z-13 |
| Enhanced Jones-Krushkal polynomial | -7w^2z-13w |
| Inner characteristic polynomial | t^5+41t^3 |
| Outer characteristic polynomial | t^6+71t^4+15t^2 |
| Flat arrow polynomial | 4*K1**2 + 2*K1*K2 + 2*K1*K3 - K1 - 3*K2 - K3 - K4 - 1 |
| 2-strand cable arrow polynomial | -48*K1**2*K2**2 + 272*K1**2*K2 - 160*K1**2*K3**2 - 596*K1**2 + 64*K1*K2*K3**3 + 704*K1*K2*K3 + 176*K1*K3*K4 + 24*K1*K4*K5 + 16*K1*K5*K6 + 8*K1*K6*K7 - 16*K2**4 - 192*K2**2*K3**2 - 8*K2**2*K4**2 + 72*K2**2*K4 - 8*K2**2*K6**2 - 474*K2**2 + 112*K2*K3*K5 + 24*K2*K4*K6 + 8*K2*K5*K7 + 8*K2*K6*K8 - 32*K3**4 - 308*K3**2 - 106*K4**2 - 40*K5**2 - 22*K6**2 - 8*K7**2 - 2*K8**2 + 530 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 5}, {2, 4}, {3}], [{2, 5}, {3, 4}, {1}], [{5}, {1, 4}, {2, 3}]] |
| If K is slice | False |