| Min(phi) over symmetries of the knot is: [-2,-1,0,0,1,2,0,0,0,1,3,0,0,1,1,0,1,0,1,1,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.1495'] |
| 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+37t^5+43t^3+10t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1495'] |
| 2-strand cable arrow polynomial of the knot is: -320*K1**4*K2**2 + 1120*K1**4*K2 - 2320*K1**4 + 384*K1**3*K2*K3 - 704*K1**3*K3 + 640*K1**2*K2**3 - 4992*K1**2*K2**2 - 640*K1**2*K2*K4 + 7952*K1**2*K2 - 208*K1**2*K3**2 - 5724*K1**2 + 96*K1*K2**3*K3 - 992*K1*K2**2*K3 - 64*K1*K2**2*K5 - 192*K1*K2*K3*K4 + 7144*K1*K2*K3 + 1264*K1*K3*K4 + 128*K1*K4*K5 - 752*K2**4 - 528*K2**2*K3**2 - 48*K2**2*K4**2 + 1432*K2**2*K4 - 4636*K2**2 + 664*K2*K3*K5 + 32*K2*K4*K6 - 2496*K3**2 - 812*K4**2 - 212*K5**2 - 4*K6**2 + 4786 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1495'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.16512', 'vk6.16603', 'vk6.18085', 'vk6.18421', 'vk6.22943', 'vk6.23038', 'vk6.24536', 'vk6.24953', 'vk6.34912', 'vk6.35019', 'vk6.36675', 'vk6.37097', 'vk6.42481', 'vk6.42592', 'vk6.43955', 'vk6.44270', 'vk6.54755', 'vk6.54850', 'vk6.55901', 'vk6.56185', 'vk6.59219', 'vk6.59282', 'vk6.60431', 'vk6.60784', 'vk6.64763', 'vk6.64824', 'vk6.65543', 'vk6.65853', 'vk6.68063', 'vk6.68126', 'vk6.68625', 'vk6.68838'] |
| 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 | O1O2O3U1O4U5U2O5O6U3U4U6 |
| R3 orbit | {'O1O2O3U1O4U5U2O5O6U3U4U6'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U4U5U1O4O6U2U6O5U3 |
| Gauss code of K* | O1O2O3U4U5U1O4U2O6O5U6U3 |
| Gauss code of -K* | O1O2O3U1U4O5O4U2O6U3U5U6 |
| 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 0 1 -1 2],[ 2 0 1 2 2 1 1],[ 0 -1 0 0 1 0 2],[ 0 -2 0 0 1 0 2],[-1 -2 -1 -1 0 -1 1],[ 1 -1 0 0 1 0 2],[-2 -1 -2 -2 -1 -2 0]] |
| Primitive based matrix | [[ 0 2 1 0 0 -1 -2],[-2 0 -1 -2 -2 -2 -1],[-1 1 0 -1 -1 -1 -2],[ 0 2 1 0 0 0 -1],[ 0 2 1 0 0 0 -2],[ 1 2 1 0 0 0 -1],[ 2 1 2 1 2 1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,0,0,1,2,1,2,2,2,1,1,1,1,2,0,0,1,0,2,1] |
| Phi over symmetry | [-2,-1,0,0,1,2,0,0,0,1,3,0,0,1,1,0,1,0,1,1,0] |
| Phi of -K | [-2,-1,0,0,1,2,0,0,1,1,3,1,1,1,1,0,0,0,0,0,0] |
| Phi of K* | [-2,-1,0,0,1,2,0,0,0,1,3,0,0,1,1,0,1,0,1,1,0] |
| Phi of -K* | [-2,-1,0,0,1,2,1,1,2,2,1,0,0,1,2,0,1,2,1,2,1] |
| 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+27t^4+19t^2 |
| Outer characteristic polynomial | t^7+37t^5+43t^3+10t |
| Flat arrow polynomial | -8*K1**2 - 4*K1*K2 + 2*K1 + 4*K2 + 2*K3 + 5 |
| 2-strand cable arrow polynomial | -320*K1**4*K2**2 + 1120*K1**4*K2 - 2320*K1**4 + 384*K1**3*K2*K3 - 704*K1**3*K3 + 640*K1**2*K2**3 - 4992*K1**2*K2**2 - 640*K1**2*K2*K4 + 7952*K1**2*K2 - 208*K1**2*K3**2 - 5724*K1**2 + 96*K1*K2**3*K3 - 992*K1*K2**2*K3 - 64*K1*K2**2*K5 - 192*K1*K2*K3*K4 + 7144*K1*K2*K3 + 1264*K1*K3*K4 + 128*K1*K4*K5 - 752*K2**4 - 528*K2**2*K3**2 - 48*K2**2*K4**2 + 1432*K2**2*K4 - 4636*K2**2 + 664*K2*K3*K5 + 32*K2*K4*K6 - 2496*K3**2 - 812*K4**2 - 212*K5**2 - 4*K6**2 + 4786 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {4, 5}, {2, 3}], [{2, 6}, {1, 5}, {3, 4}], [{2, 6}, {3, 5}, {1, 4}], [{4, 6}, {2, 5}, {1, 3}]] |
| If K is slice | False |