| Min(phi) over symmetries of the knot is: [-3,-2,0,1,1,3,-1,2,1,3,4,1,1,2,2,0,0,1,0,0,2] |
| Flat knots (up to 7 crossings) with same phi are :['6.556'] |
| Arrow polynomial of the knot is: -6*K1**2 - 4*K1*K2 + 2*K1 + 3*K2 + 2*K3 + 4 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.239', '6.428', '6.470', '6.556', '6.700', '6.910', '6.962', '6.1006', '6.1013', '6.1038', '6.1207', '6.1224', '6.1225', '6.1269', '6.1270', '6.1308', '6.1319', '6.1320', '6.1323', '6.1485', '6.1551', '6.1579', '6.1581', '6.1660', '6.1672', '6.1679', '6.1711', '6.1719', '6.1732', '6.1745', '6.1748', '6.1827', '6.1836', '6.1838', '6.1850', '6.1866'] |
| Outer characteristic polynomial of the knot is: t^7+70t^5+60t^3+8t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.556'] |
| 2-strand cable arrow polynomial of the knot is: -64*K1**6 + 1120*K1**4*K2 - 4256*K1**4 + 672*K1**3*K2*K3 + 32*K1**3*K3*K4 - 992*K1**3*K3 - 4048*K1**2*K2**2 - 448*K1**2*K2*K4 + 9536*K1**2*K2 - 1280*K1**2*K3**2 - 160*K1**2*K4**2 - 32*K1**2*K5**2 - 6356*K1**2 - 512*K1*K2**2*K3 - 160*K1*K2*K3*K4 - 32*K1*K2*K3*K6 + 7184*K1*K2*K3 - 32*K1*K2*K4*K5 + 2248*K1*K3*K4 + 440*K1*K4*K5 + 112*K1*K5*K6 - 216*K2**4 - 176*K2**2*K3**2 - 48*K2**2*K4**2 + 920*K2**2*K4 - 5460*K2**2 + 608*K2*K3*K5 + 128*K2*K4*K6 + 32*K3**2*K6 - 3008*K3**2 - 1182*K4**2 - 428*K5**2 - 100*K6**2 + 5956 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.556'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.20028', 'vk6.20073', 'vk6.21300', 'vk6.21353', 'vk6.27075', 'vk6.27138', 'vk6.28780', 'vk6.28825', 'vk6.38468', 'vk6.38531', 'vk6.40657', 'vk6.40726', 'vk6.45348', 'vk6.45431', 'vk6.47117', 'vk6.47171', 'vk6.56827', 'vk6.56878', 'vk6.57961', 'vk6.58014', 'vk6.61341', 'vk6.61408', 'vk6.62517', 'vk6.62563', 'vk6.66539', 'vk6.66578', 'vk6.67328', 'vk6.67367', 'vk6.69181', 'vk6.69230', 'vk6.69932', 'vk6.69969'] |
| 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 | O1O2O3O4O5U4U1U3O6U2U5U6 |
| R3 orbit | {'O1O2O3O4O5U4U1U3O6U2U5U6'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4O5U6U1U4O6U3U5U2 |
| Gauss code of K* | O1O2O3U4O5O6O4U2U5U3U1U6 |
| Gauss code of -K* | O1O2O3U1O4O5O6U2U6U4U3U5 |
| 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 -3 -1 0 -1 3 2],[ 3 0 2 1 0 4 2],[ 1 -2 0 0 0 3 2],[ 0 -1 0 0 0 2 1],[ 1 0 0 0 0 1 1],[-3 -4 -3 -2 -1 0 1],[-2 -2 -2 -1 -1 -1 0]] |
| Primitive based matrix | [[ 0 3 2 0 -1 -1 -3],[-3 0 1 -2 -1 -3 -4],[-2 -1 0 -1 -1 -2 -2],[ 0 2 1 0 0 0 -1],[ 1 1 1 0 0 0 0],[ 1 3 2 0 0 0 -2],[ 3 4 2 1 0 2 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-3,-2,0,1,1,3,-1,2,1,3,4,1,1,2,2,0,0,1,0,0,2] |
| Phi over symmetry | [-3,-2,0,1,1,3,-1,2,1,3,4,1,1,2,2,0,0,1,0,0,2] |
| Phi of -K | [-3,-1,-1,0,2,3,0,2,2,3,2,0,1,1,1,1,2,3,1,1,2] |
| Phi of K* | [-3,-2,0,1,1,3,2,1,1,3,2,1,1,2,3,1,1,2,0,0,2] |
| Phi of -K* | [-3,-1,-1,0,2,3,0,2,1,2,4,0,0,1,1,0,2,3,1,2,-1] |
| Symmetry type of based matrix | c |
| u-polynomial | -t^2+2t |
| Normalized Jones-Krushkal polynomial | z^2+22z+41 |
| Enhanced Jones-Krushkal polynomial | w^3z^2+22w^2z+41w |
| Inner characteristic polynomial | t^6+46t^4+19t^2+1 |
| Outer characteristic polynomial | t^7+70t^5+60t^3+8t |
| Flat arrow polynomial | -6*K1**2 - 4*K1*K2 + 2*K1 + 3*K2 + 2*K3 + 4 |
| 2-strand cable arrow polynomial | -64*K1**6 + 1120*K1**4*K2 - 4256*K1**4 + 672*K1**3*K2*K3 + 32*K1**3*K3*K4 - 992*K1**3*K3 - 4048*K1**2*K2**2 - 448*K1**2*K2*K4 + 9536*K1**2*K2 - 1280*K1**2*K3**2 - 160*K1**2*K4**2 - 32*K1**2*K5**2 - 6356*K1**2 - 512*K1*K2**2*K3 - 160*K1*K2*K3*K4 - 32*K1*K2*K3*K6 + 7184*K1*K2*K3 - 32*K1*K2*K4*K5 + 2248*K1*K3*K4 + 440*K1*K4*K5 + 112*K1*K5*K6 - 216*K2**4 - 176*K2**2*K3**2 - 48*K2**2*K4**2 + 920*K2**2*K4 - 5460*K2**2 + 608*K2*K3*K5 + 128*K2*K4*K6 + 32*K3**2*K6 - 3008*K3**2 - 1182*K4**2 - 428*K5**2 - 100*K6**2 + 5956 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{2, 6}, {1, 5}, {3, 4}], [{3, 6}, {1, 5}, {2, 4}], [{4, 6}, {1, 5}, {2, 3}]] |
| If K is slice | False |