| Min(phi) over symmetries of the knot is: [-2,-1,-1,1,1,2,-1,0,1,2,2,1,1,1,0,2,1,2,0,1,1] |
| Flat knots (up to 7 crossings) with same phi are :['6.1641'] |
| Arrow polynomial of the knot is: 4*K1**3 - 4*K1**2 - 4*K1*K2 - K1 + 2*K2 + K3 + 3 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.209', '6.231', '6.391', '6.419', '6.600', '6.661', '6.744', '6.812', '6.826', '6.1114', '6.1125', '6.1202', '6.1275', '6.1292', '6.1305', '6.1322', '6.1365', '6.1481', '6.1483', '6.1497', '6.1543', '6.1549', '6.1572', '6.1577', '6.1580', '6.1594', '6.1641', '6.1658', '6.1683', '6.1753', '6.1830', '6.1907', '6.1928'] |
| Outer characteristic polynomial of the knot is: t^7+36t^5+57t^3+13t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1641'] |
| 2-strand cable arrow polynomial of the knot is: -64*K1**6 + 960*K1**4*K2 - 3408*K1**4 + 256*K1**3*K2*K3 + 32*K1**3*K3*K4 - 608*K1**3*K3 - 192*K1**2*K2**4 + 480*K1**2*K2**3 + 224*K1**2*K2**2*K4 - 4576*K1**2*K2**2 + 64*K1**2*K2*K3**2 - 256*K1**2*K2*K4 + 8736*K1**2*K2 - 848*K1**2*K3**2 - 80*K1**2*K4**2 - 5316*K1**2 + 448*K1*K2**3*K3 - 1056*K1*K2**2*K3 - 512*K1*K2**2*K5 - 192*K1*K2*K3*K4 + 6696*K1*K2*K3 + 1024*K1*K3*K4 + 216*K1*K4*K5 - 32*K2**6 + 64*K2**4*K4 - 576*K2**4 - 32*K2**3*K6 - 224*K2**2*K3**2 - 16*K2**2*K4**2 + 1416*K2**2*K4 - 4902*K2**2 + 344*K2*K3*K5 + 16*K2*K4*K6 - 2036*K3**2 - 632*K4**2 - 112*K5**2 - 2*K6**2 + 4694 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1641'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.13871', 'vk6.13968', 'vk6.14127', 'vk6.14350', 'vk6.14946', 'vk6.15069', 'vk6.15579', 'vk6.16049', 'vk6.16302', 'vk6.16325', 'vk6.17426', 'vk6.22613', 'vk6.22644', 'vk6.23938', 'vk6.33690', 'vk6.33768', 'vk6.34142', 'vk6.34254', 'vk6.34599', 'vk6.36209', 'vk6.36238', 'vk6.42296', 'vk6.53849', 'vk6.53897', 'vk6.54088', 'vk6.54390', 'vk6.54583', 'vk6.55582', 'vk6.59028', 'vk6.59055', 'vk6.60072', 'vk6.64548'] |
| 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 | O1O2O3U1O4U2U5U3O5O6U4U6 |
| R3 orbit | {'O1O2O3U1O4U2U5U3O5O6U4U6'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U4U5O4O6U1U6U2O5U3 |
| Gauss code of K* | O1O2O3U2U4O5O4U6U1U3O6U5 |
| Gauss code of -K* | O1O2O3U4O5U1U3U5O6O4U6U2 |
| Diagrammatic symmetry type | c |
| Flat genus of the diagram | 3 |
| If K is checkerboard colorable | False |
| If K is almost classical | False |
| Based matrix from Gauss code | [[ 0 -2 -1 2 1 -1 1],[ 2 0 1 2 2 1 0],[ 1 -1 0 1 2 0 1],[-2 -2 -1 0 0 -2 1],[-1 -2 -2 0 0 -1 1],[ 1 -1 0 2 1 0 1],[-1 0 -1 -1 -1 -1 0]] |
| Primitive based matrix | [[ 0 2 1 1 -1 -1 -2],[-2 0 1 0 -1 -2 -2],[-1 -1 0 -1 -1 -1 0],[-1 0 1 0 -2 -1 -2],[ 1 1 1 2 0 0 -1],[ 1 2 1 1 0 0 -1],[ 2 2 0 2 1 1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,-1,1,1,2,-1,0,1,2,2,1,1,1,0,2,1,2,0,1,1] |
| Phi over symmetry | [-2,-1,-1,1,1,2,-1,0,1,2,2,1,1,1,0,2,1,2,0,1,1] |
| Phi of -K | [-2,-1,-1,1,1,2,0,0,1,3,2,0,0,1,2,1,1,1,-1,1,2] |
| Phi of K* | [-2,-1,-1,1,1,2,1,2,1,2,2,1,1,0,1,1,1,3,0,0,0] |
| Phi of -K* | [-2,-1,-1,1,1,2,1,1,0,2,2,0,1,1,2,1,2,1,-1,-1,0] |
| Symmetry type of based matrix | c |
| u-polynomial | 0 |
| Normalized Jones-Krushkal polynomial | 3z^2+22z+33 |
| Enhanced Jones-Krushkal polynomial | 3w^3z^2-2w^3z+24w^2z+33w |
| Inner characteristic polynomial | t^6+24t^4+27t^2+4 |
| Outer characteristic polynomial | t^7+36t^5+57t^3+13t |
| Flat arrow polynomial | 4*K1**3 - 4*K1**2 - 4*K1*K2 - K1 + 2*K2 + K3 + 3 |
| 2-strand cable arrow polynomial | -64*K1**6 + 960*K1**4*K2 - 3408*K1**4 + 256*K1**3*K2*K3 + 32*K1**3*K3*K4 - 608*K1**3*K3 - 192*K1**2*K2**4 + 480*K1**2*K2**3 + 224*K1**2*K2**2*K4 - 4576*K1**2*K2**2 + 64*K1**2*K2*K3**2 - 256*K1**2*K2*K4 + 8736*K1**2*K2 - 848*K1**2*K3**2 - 80*K1**2*K4**2 - 5316*K1**2 + 448*K1*K2**3*K3 - 1056*K1*K2**2*K3 - 512*K1*K2**2*K5 - 192*K1*K2*K3*K4 + 6696*K1*K2*K3 + 1024*K1*K3*K4 + 216*K1*K4*K5 - 32*K2**6 + 64*K2**4*K4 - 576*K2**4 - 32*K2**3*K6 - 224*K2**2*K3**2 - 16*K2**2*K4**2 + 1416*K2**2*K4 - 4902*K2**2 + 344*K2*K3*K5 + 16*K2*K4*K6 - 2036*K3**2 - 632*K4**2 - 112*K5**2 - 2*K6**2 + 4694 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{2, 6}, {4, 5}, {1, 3}], [{5, 6}, {2, 4}, {1, 3}]] |
| If K is slice | False |