| Min(phi) over symmetries of the knot is: [-3,-1,0,2,2,0,2,2,4,1,0,1,1,1,-1] |
| Flat knots (up to 7 crossings) with same phi are :['6.639'] |
| Arrow polynomial of the knot is: 4*K1**3 - 8*K1**2 - 2*K1*K2 - 2*K1 + 4*K2 + 5 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.635', '6.639', '6.659', '6.727', '6.732', '6.735', '6.799', '6.1088', '6.1090', '6.1095', '6.1383'] |
| Outer characteristic polynomial of the knot is: t^6+49t^4+16t^2 |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.639'] |
| 2-strand cable arrow polynomial of the knot is: 96*K1**4*K2 - 1184*K1**4 - 256*K1**2*K2**4 + 704*K1**2*K2**3 - 2544*K1**2*K2**2 + 4144*K1**2*K2 - 96*K1**2*K3**2 - 2652*K1**2 + 256*K1*K2**3*K3 + 1984*K1*K2*K3 + 184*K1*K3*K4 + 16*K1*K4*K5 - 32*K2**6 + 32*K2**4*K4 - 640*K2**4 - 96*K2**2*K3**2 - 8*K2**2*K4**2 + 216*K2**2*K4 - 1400*K2**2 + 16*K2*K3*K5 - 564*K3**2 - 112*K4**2 - 8*K5**2 + 1942 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.639'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.73363', 'vk6.73379', 'vk6.73525', 'vk6.73558', 'vk6.73726', 'vk6.73845', 'vk6.74258', 'vk6.74884', 'vk6.75318', 'vk6.75535', 'vk6.75845', 'vk6.76435', 'vk6.78253', 'vk6.78300', 'vk6.78505', 'vk6.78642', 'vk6.78837', 'vk6.79302', 'vk6.80074', 'vk6.80086', 'vk6.80223', 'vk6.80268', 'vk6.80400', 'vk6.80767', 'vk6.81958', 'vk6.82689', 'vk6.84749', 'vk6.85049', 'vk6.85161', 'vk6.86532', 'vk6.87346', 'vk6.89441'] |
| 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 | O1O2O3O4U1O5U4U2O6U3U5U6 |
| R3 orbit | {'O1O2O3O4U1O5U4U2O6U3U5U6'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U5U6U2O5U3U1O6U4 |
| Gauss code of K* | O1O2O3U4U5U1U6O4U2O6O5U3 |
| Gauss code of -K* | O1O2O3U1O4O5U2O6U5U3U4U6 |
| Diagrammatic symmetry type | c |
| Flat genus of the diagram | 2 |
| If K is checkerboard colorable | False |
| If K is almost classical | False |
| Based matrix from Gauss code | [[ 0 -3 -1 0 0 2 2],[ 3 0 2 3 1 3 1],[ 1 -2 0 1 0 3 2],[ 0 -3 -1 0 0 2 2],[ 0 -1 0 0 0 1 1],[-2 -3 -3 -2 -1 0 1],[-2 -1 -2 -2 -1 -1 0]] |
| Primitive based matrix | [[ 0 2 2 0 -1 -3],[-2 0 1 -1 -3 -3],[-2 -1 0 -1 -2 -1],[ 0 1 1 0 0 -1],[ 1 3 2 0 0 -2],[ 3 3 1 1 2 0]] |
| If based matrix primitive | False |
| Phi of primitive based matrix | [-2,-2,0,1,3,-1,1,3,3,1,2,1,0,1,2] |
| Phi over symmetry | [-3,-1,0,2,2,0,2,2,4,1,0,1,1,1,-1] |
| Phi of -K | [-3,-1,0,2,2,0,2,2,4,1,0,1,1,1,-1] |
| Phi of K* | [-2,-2,0,1,3,-1,1,1,4,1,0,2,1,2,0] |
| Phi of -K* | [-3,-1,0,2,2,2,1,1,3,0,2,3,1,1,-1] |
| Symmetry type of based matrix | c |
| u-polynomial | t^3-2t^2+t |
| Normalized Jones-Krushkal polynomial | 11z+23 |
| Enhanced Jones-Krushkal polynomial | -4w^3z+15w^2z+23w |
| Inner characteristic polynomial | t^5+31t^3+4t |
| Outer characteristic polynomial | t^6+49t^4+16t^2 |
| Flat arrow polynomial | 4*K1**3 - 8*K1**2 - 2*K1*K2 - 2*K1 + 4*K2 + 5 |
| 2-strand cable arrow polynomial | 96*K1**4*K2 - 1184*K1**4 - 256*K1**2*K2**4 + 704*K1**2*K2**3 - 2544*K1**2*K2**2 + 4144*K1**2*K2 - 96*K1**2*K3**2 - 2652*K1**2 + 256*K1*K2**3*K3 + 1984*K1*K2*K3 + 184*K1*K3*K4 + 16*K1*K4*K5 - 32*K2**6 + 32*K2**4*K4 - 640*K2**4 - 96*K2**2*K3**2 - 8*K2**2*K4**2 + 216*K2**2*K4 - 1400*K2**2 + 16*K2*K3*K5 - 564*K3**2 - 112*K4**2 - 8*K5**2 + 1942 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{3, 6}, {4, 5}, {1, 2}], [{6}, {4, 5}, {3}, {1, 2}]] |
| If K is slice | False |