| Min(phi) over symmetries of the knot is: [-2,-1,0,0,1,2,0,0,1,2,2,1,0,2,1,0,1,1,0,1,1] |
| Flat knots (up to 7 crossings) with same phi are :['6.1717'] |
| Arrow polynomial of the knot is: -8*K1**2 - 4*K1*K2 + 2*K1 + 4*K2 + 2*K3 + 5 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.235', '6.379', '6.411', '6.547', '6.811', '6.818', '6.823', '6.897', '6.898', '6.1008', '6.1053', '6.1109', '6.1110', '6.1130', '6.1222', '6.1239', '6.1303', '6.1307', '6.1342', '6.1491', '6.1495', '6.1496', '6.1519', '6.1592', '6.1593', '6.1642', '6.1652', '6.1653', '6.1671', '6.1673', '6.1717'] |
| Outer characteristic polynomial of the knot is: t^7+29t^5+61t^3+10t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1717'] |
| 2-strand cable arrow polynomial of the knot is: -64*K1**6 + 352*K1**4*K2 - 3584*K1**4 + 128*K1**3*K2*K3 + 64*K1**3*K3*K4 - 192*K1**3*K3 + 384*K1**2*K2**3 - 5168*K1**2*K2**2 - 992*K1**2*K2*K4 + 8760*K1**2*K2 - 1184*K1**2*K3**2 - 32*K1**2*K3*K5 - 336*K1**2*K4**2 - 5536*K1**2 - 416*K1*K2**2*K3 - 32*K1*K2**2*K5 - 128*K1*K2*K3*K4 + 7544*K1*K2*K3 + 2784*K1*K3*K4 + 496*K1*K4*K5 - 864*K2**4 - 96*K2**2*K3**2 - 16*K2**2*K4**2 + 1472*K2**2*K4 - 4596*K2**2 + 336*K2*K3*K5 + 32*K2*K4*K6 - 2820*K3**2 - 1384*K4**2 - 268*K5**2 - 12*K6**2 + 5366 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1717'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.16940', 'vk6.17183', 'vk6.20548', 'vk6.21947', 'vk6.23336', 'vk6.23631', 'vk6.28002', 'vk6.29467', 'vk6.35384', 'vk6.35805', 'vk6.39414', 'vk6.41605', 'vk6.42857', 'vk6.43136', 'vk6.45990', 'vk6.47664', 'vk6.55091', 'vk6.55344', 'vk6.57428', 'vk6.58597', 'vk6.59489', 'vk6.59781', 'vk6.62095', 'vk6.63071', 'vk6.64940', 'vk6.65148', 'vk6.66968', 'vk6.67827', 'vk6.68229', 'vk6.68372', 'vk6.69579', 'vk6.70274'] |
| 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 | O1O2O3U1U4O5O6U5U2O4U3U6 |
| R3 orbit | {'O1O2O3U1U4O5O6U5U2O4U3U6'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U4U1O5U2U6O4O6U5U3 |
| Gauss code of K* | O1O2U3O4O5U6U2U4O6O3U1U5 |
| Gauss code of -K* | O1O2U3O4O5U1U5O3O6U2U4U6 |
| 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 0 1 0 -1 2],[ 2 0 1 2 1 0 2],[ 0 -1 0 0 0 0 2],[-1 -2 0 0 -1 0 1],[ 0 -1 0 1 0 -1 1],[ 1 0 0 0 1 0 1],[-2 -2 -2 -1 -1 -1 0]] |
| Primitive based matrix | [[ 0 2 1 0 0 -1 -2],[-2 0 -1 -1 -2 -1 -2],[-1 1 0 -1 0 0 -2],[ 0 1 1 0 0 -1 -1],[ 0 2 0 0 0 0 -1],[ 1 1 0 1 0 0 0],[ 2 2 2 1 1 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,0,0,1,2,1,1,2,1,2,1,0,0,2,0,1,1,0,1,0] |
| Phi over symmetry | [-2,-1,0,0,1,2,0,0,1,2,2,1,0,2,1,0,1,1,0,1,1] |
| Phi of -K | [-2,-1,0,0,1,2,1,1,1,1,2,0,1,2,2,0,0,1,1,0,0] |
| Phi of K* | [-2,-1,0,0,1,2,0,0,1,2,2,1,0,2,1,0,1,1,0,1,1] |
| Phi of -K* | [-2,-1,0,0,1,2,0,1,1,2,2,0,1,0,1,0,0,2,1,1,1] |
| Symmetry type of based matrix | c |
| u-polynomial | 0 |
| Normalized Jones-Krushkal polynomial | 3z^2+24z+37 |
| Enhanced Jones-Krushkal polynomial | 3w^3z^2+24w^2z+37w |
| Inner characteristic polynomial | t^6+19t^4+35t^2+4 |
| Outer characteristic polynomial | t^7+29t^5+61t^3+10t |
| Flat arrow polynomial | -8*K1**2 - 4*K1*K2 + 2*K1 + 4*K2 + 2*K3 + 5 |
| 2-strand cable arrow polynomial | -64*K1**6 + 352*K1**4*K2 - 3584*K1**4 + 128*K1**3*K2*K3 + 64*K1**3*K3*K4 - 192*K1**3*K3 + 384*K1**2*K2**3 - 5168*K1**2*K2**2 - 992*K1**2*K2*K4 + 8760*K1**2*K2 - 1184*K1**2*K3**2 - 32*K1**2*K3*K5 - 336*K1**2*K4**2 - 5536*K1**2 - 416*K1*K2**2*K3 - 32*K1*K2**2*K5 - 128*K1*K2*K3*K4 + 7544*K1*K2*K3 + 2784*K1*K3*K4 + 496*K1*K4*K5 - 864*K2**4 - 96*K2**2*K3**2 - 16*K2**2*K4**2 + 1472*K2**2*K4 - 4596*K2**2 + 336*K2*K3*K5 + 32*K2*K4*K6 - 2820*K3**2 - 1384*K4**2 - 268*K5**2 - 12*K6**2 + 5366 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {3, 5}, {2, 4}], [{1, 6}, {3, 5}, {4}, {2}], [{2, 6}, {3, 5}, {1, 4}], [{2, 6}, {3, 5}, {4}, {1}], [{3, 6}, {2, 5}, {1, 4}], [{4, 6}, {3, 5}, {1, 2}], [{6}, {3, 5}, {4}, {1, 2}]] |
| If K is slice | False |