| Min(phi) over symmetries of the knot is: [-2,-2,0,1,1,2,0,1,0,2,1,1,0,3,2,1,-1,0,-1,0,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.1049'] |
| Arrow polynomial of the knot is: 4*K1**3 - 2*K1**2 - 4*K1*K2 - K1 + K2 + K3 + 2 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.568', '6.806', '6.1000', '6.1049', '6.1081', '6.1101', '6.1112', '6.1122', '6.1193', '6.1195', '6.1208', '6.1235', '6.1263', '6.1517', '6.1528', '6.1537', '6.1542', '6.1545', '6.1558', '6.1569', '6.1575', '6.1644', '6.1650', '6.1681', '6.1692', '6.1702', '6.1706', '6.1728', '6.1734', '6.1739', '6.1799', '6.1813', '6.1820', '6.1834', '6.1840', '6.1851', '6.1861', '6.1878'] |
| Outer characteristic polynomial of the knot is: t^7+59t^5+307t^3+4t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1049'] |
| 2-strand cable arrow polynomial of the knot is: 96*K1**4*K2 - 128*K1**4 - 64*K1**3*K3 - 192*K1**2*K2**4 + 224*K1**2*K2**3 + 160*K1**2*K2**2*K4 - 3632*K1**2*K2**2 - 512*K1**2*K2*K4 + 4480*K1**2*K2 - 192*K1**2*K4**2 - 3544*K1**2 + 288*K1*K2**3*K3 - 800*K1*K2**2*K3 - 352*K1*K2**2*K5 + 4360*K1*K2*K3 + 856*K1*K3*K4 + 136*K1*K4*K5 - 32*K2**6 + 64*K2**4*K4 - 792*K2**4 - 32*K2**3*K6 - 112*K2**2*K3**2 - 16*K2**2*K4**2 + 1400*K2**2*K4 - 2654*K2**2 + 248*K2*K3*K5 + 16*K2*K4*K6 - 1248*K3**2 - 562*K4**2 - 72*K5**2 - 2*K6**2 + 2608 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1049'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.4727', 'vk6.5047', 'vk6.6257', 'vk6.6704', 'vk6.8228', 'vk6.8671', 'vk6.9615', 'vk6.9937', 'vk6.20653', 'vk6.22086', 'vk6.28143', 'vk6.29574', 'vk6.39581', 'vk6.41814', 'vk6.46200', 'vk6.47820', 'vk6.48767', 'vk6.48973', 'vk6.49573', 'vk6.49782', 'vk6.50781', 'vk6.50992', 'vk6.51267', 'vk6.51467', 'vk6.57577', 'vk6.58745', 'vk6.62251', 'vk6.63199', 'vk6.67047', 'vk6.67922', 'vk6.69676', 'vk6.70359'] |
| 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 | O1O2O3O4U5U6O5U2O6U1U4U3 |
| R3 orbit | {'O1O2O3O4U5U6O5U2O6U1U4U3'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U2U1U4O5U3O6U5U6 |
| Gauss code of K* | O1O2O3U1U4U3U2O5O6U5O4U6 |
| Gauss code of -K* | O1O2O3U4O5U6O4O6U2U1U5U3 |
| 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 2 -1 0],[ 2 0 1 3 2 1 2],[ 1 -1 0 1 0 1 2],[-2 -3 -1 0 0 -3 -1],[-2 -2 0 0 0 -3 -1],[ 1 -1 -1 3 3 0 0],[ 0 -2 -2 1 1 0 0]] |
| Primitive based matrix | [[ 0 2 2 0 -1 -1 -2],[-2 0 0 -1 0 -3 -2],[-2 0 0 -1 -1 -3 -3],[ 0 1 1 0 -2 0 -2],[ 1 0 1 2 0 1 -1],[ 1 3 3 0 -1 0 -1],[ 2 2 3 2 1 1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-2,0,1,1,2,0,1,0,3,2,1,1,3,3,2,0,2,-1,1,1] |
| Phi over symmetry | [-2,-2,0,1,1,2,0,1,0,2,1,1,0,3,2,1,-1,0,-1,0,0] |
| Phi of -K | [-2,-1,-1,0,2,2,0,0,0,1,2,-1,-1,2,3,1,0,0,1,1,0] |
| Phi of K* | [-2,-2,0,1,1,2,0,1,0,2,1,1,0,3,2,1,-1,0,-1,0,0] |
| Phi of -K* | [-2,-1,-1,0,2,2,1,1,2,2,3,-1,0,3,3,2,0,1,1,1,0] |
| Symmetry type of based matrix | c |
| u-polynomial | -t^2+2t |
| Normalized Jones-Krushkal polynomial | 7z^2+24z+21 |
| Enhanced Jones-Krushkal polynomial | 7w^3z^2+24w^2z+21w |
| Inner characteristic polynomial | t^6+45t^4+224t^2 |
| Outer characteristic polynomial | t^7+59t^5+307t^3+4t |
| Flat arrow polynomial | 4*K1**3 - 2*K1**2 - 4*K1*K2 - K1 + K2 + K3 + 2 |
| 2-strand cable arrow polynomial | 96*K1**4*K2 - 128*K1**4 - 64*K1**3*K3 - 192*K1**2*K2**4 + 224*K1**2*K2**3 + 160*K1**2*K2**2*K4 - 3632*K1**2*K2**2 - 512*K1**2*K2*K4 + 4480*K1**2*K2 - 192*K1**2*K4**2 - 3544*K1**2 + 288*K1*K2**3*K3 - 800*K1*K2**2*K3 - 352*K1*K2**2*K5 + 4360*K1*K2*K3 + 856*K1*K3*K4 + 136*K1*K4*K5 - 32*K2**6 + 64*K2**4*K4 - 792*K2**4 - 32*K2**3*K6 - 112*K2**2*K3**2 - 16*K2**2*K4**2 + 1400*K2**2*K4 - 2654*K2**2 + 248*K2*K3*K5 + 16*K2*K4*K6 - 1248*K3**2 - 562*K4**2 - 72*K5**2 - 2*K6**2 + 2608 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {2, 5}, {3, 4}], [{4, 6}, {3, 5}, {1, 2}]] |
| If K is slice | False |