| Min(phi) over symmetries of the knot is: [-2,-1,-1,1,1,2,-1,-1,2,2,2,0,1,1,1,1,2,1,1,1,1] |
| Flat knots (up to 7 crossings) with same phi are :['6.401'] |
| Arrow polynomial of the knot is: -4*K1**2 - 4*K1*K2 + 2*K1 + 2*K2 + 2*K3 + 3 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.65', '6.137', '6.201', '6.203', '6.214', '6.310', '6.314', '6.332', '6.385', '6.386', '6.401', '6.516', '6.564', '6.571', '6.572', '6.578', '6.621', '6.626', '6.716', '6.773', '6.807', '6.814', '6.821', '6.940', '6.966', '6.1036', '6.1071', '6.1108', '6.1111', '6.1131', '6.1188', '6.1203', '6.1206', '6.1220', '6.1340', '6.1387', '6.1548', '6.1663', '6.1680', '6.1693', '6.1831', '6.1932'] |
| Outer characteristic polynomial of the knot is: t^7+38t^5+60t^3+14t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.401'] |
| 2-strand cable arrow polynomial of the knot is: 160*K1**4*K2 - 912*K1**4 + 160*K1**3*K2*K3 - 256*K1**3*K3 + 128*K1**2*K2**3 - 3600*K1**2*K2**2 + 96*K1**2*K2*K3**2 - 64*K1**2*K2*K4 + 5648*K1**2*K2 - 496*K1**2*K3**2 - 32*K1**2*K4**2 - 4912*K1**2 + 128*K1*K2**3*K3 - 768*K1*K2**2*K3 - 64*K1*K2**2*K5 - 224*K1*K2*K3*K4 + 6144*K1*K2*K3 + 1072*K1*K3*K4 + 184*K1*K4*K5 - 592*K2**4 - 368*K2**2*K3**2 - 48*K2**2*K4**2 + 1392*K2**2*K4 - 4220*K2**2 + 592*K2*K3*K5 + 32*K2*K4*K6 - 2372*K3**2 - 824*K4**2 - 244*K5**2 - 4*K6**2 + 4262 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.401'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.3630', 'vk6.3717', 'vk6.3908', 'vk6.4013', 'vk6.7052', 'vk6.7105', 'vk6.7280', 'vk6.7383', 'vk6.11388', 'vk6.12571', 'vk6.12682', 'vk6.19115', 'vk6.19160', 'vk6.19821', 'vk6.25724', 'vk6.25783', 'vk6.26254', 'vk6.26699', 'vk6.30996', 'vk6.31123', 'vk6.32176', 'vk6.37843', 'vk6.37898', 'vk6.44975', 'vk6.48258', 'vk6.48437', 'vk6.50014', 'vk6.50157', 'vk6.52146', 'vk6.63727', 'vk6.66208', 'vk6.66235'] |
| 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 | O1O2O3O4O5U4U3O6U5U1U6U2 |
| R3 orbit | {'O1O2O3O4O5U4U3O6U5U1U6U2'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4O5U4U6U5U1O6U3U2 |
| Gauss code of K* | O1O2O3O4U2U4U5U6U1O6O5U3 |
| Gauss code of -K* | O1O2O3O4U2O5O6U4U6U5U1U3 |
| 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 -1 -1 1 2],[ 2 0 2 -1 -1 2 2],[-1 -2 0 -1 -1 1 1],[ 1 1 1 0 0 2 1],[ 1 1 1 0 0 1 1],[-1 -2 -1 -2 -1 0 1],[-2 -2 -1 -1 -1 -1 0]] |
| Primitive based matrix | [[ 0 2 1 1 -1 -1 -2],[-2 0 -1 -1 -1 -1 -2],[-1 1 0 1 -1 -1 -2],[-1 1 -1 0 -1 -2 -2],[ 1 1 1 1 0 0 1],[ 1 1 1 2 0 0 1],[ 2 2 2 2 -1 -1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,-1,1,1,2,1,1,1,1,2,-1,1,1,2,1,2,2,0,-1,-1] |
| Phi over symmetry | [-2,-1,-1,1,1,2,-1,-1,2,2,2,0,1,1,1,1,2,1,1,1,1] |
| Phi of -K | [-2,-1,-1,1,1,2,2,2,1,1,2,0,0,1,2,1,1,2,1,0,0] |
| Phi of K* | [-2,-1,-1,1,1,2,0,0,2,2,2,-1,0,1,1,1,1,1,0,2,2] |
| Phi of -K* | [-2,-1,-1,1,1,2,-1,-1,2,2,2,0,1,1,1,1,2,1,1,1,1] |
| Symmetry type of based matrix | c |
| u-polynomial | 0 |
| Normalized Jones-Krushkal polynomial | 6z^2+27z+31 |
| Enhanced Jones-Krushkal polynomial | 6w^3z^2+27w^2z+31w |
| Inner characteristic polynomial | t^6+26t^4+22t^2+1 |
| Outer characteristic polynomial | t^7+38t^5+60t^3+14t |
| Flat arrow polynomial | -4*K1**2 - 4*K1*K2 + 2*K1 + 2*K2 + 2*K3 + 3 |
| 2-strand cable arrow polynomial | 160*K1**4*K2 - 912*K1**4 + 160*K1**3*K2*K3 - 256*K1**3*K3 + 128*K1**2*K2**3 - 3600*K1**2*K2**2 + 96*K1**2*K2*K3**2 - 64*K1**2*K2*K4 + 5648*K1**2*K2 - 496*K1**2*K3**2 - 32*K1**2*K4**2 - 4912*K1**2 + 128*K1*K2**3*K3 - 768*K1*K2**2*K3 - 64*K1*K2**2*K5 - 224*K1*K2*K3*K4 + 6144*K1*K2*K3 + 1072*K1*K3*K4 + 184*K1*K4*K5 - 592*K2**4 - 368*K2**2*K3**2 - 48*K2**2*K4**2 + 1392*K2**2*K4 - 4220*K2**2 + 592*K2*K3*K5 + 32*K2*K4*K6 - 2372*K3**2 - 824*K4**2 - 244*K5**2 - 4*K6**2 + 4262 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {3, 5}, {2, 4}], [{1, 6}, {4, 5}, {2, 3}], [{2, 6}, {3, 5}, {1, 4}], [{4, 6}, {3, 5}, {1, 2}]] |
| If K is slice | False |