| Min(phi) over symmetries of the knot is: [-2,-2,0,1,1,2,-2,1,1,1,3,1,0,1,2,0,1,1,0,-1,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.755'] |
| Arrow polynomial of the knot is: -10*K1**2 - 4*K1*K2 + 2*K1 + 5*K2 + 2*K3 + 6 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.425', '6.655', '6.755', '6.769', '6.792', '6.1240', '6.1494', '6.1522', '6.1534', '6.1587', '6.1707', '6.1746', '6.1747', '6.1786', '6.1814', '6.1828', '6.1835', '6.1854', '6.1870'] |
| Outer characteristic polynomial of the knot is: t^7+53t^5+52t^3+5t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.755'] |
| 2-strand cable arrow polynomial of the knot is: -64*K1**4*K2**2 + 384*K1**4*K2 - 1792*K1**4 + 160*K1**3*K2*K3 - 800*K1**3*K3 + 64*K1**2*K2**3 - 2000*K1**2*K2**2 + 192*K1**2*K2*K3**2 - 160*K1**2*K2*K4 + 6448*K1**2*K2 - 608*K1**2*K3**2 - 32*K1**2*K3*K5 - 5136*K1**2 - 576*K1*K2**2*K3 - 32*K1*K2**2*K5 - 192*K1*K2*K3*K4 + 5056*K1*K2*K3 + 872*K1*K3*K4 + 96*K1*K4*K5 - 136*K2**4 - 208*K2**2*K3**2 - 48*K2**2*K4**2 + 600*K2**2*K4 - 3900*K2**2 + 256*K2*K3*K5 + 32*K2*K4*K6 - 1844*K3**2 - 406*K4**2 - 84*K5**2 - 4*K6**2 + 3860 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.755'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.3568', 'vk6.3590', 'vk6.3604', 'vk6.3811', 'vk6.3829', 'vk6.3844', 'vk6.3862', 'vk6.6977', 'vk6.6991', 'vk6.7010', 'vk6.7024', 'vk6.7195', 'vk6.7213', 'vk6.7227', 'vk6.15329', 'vk6.15349', 'vk6.15454', 'vk6.15474', 'vk6.33974', 'vk6.34018', 'vk6.34030', 'vk6.34429', 'vk6.48214', 'vk6.48228', 'vk6.48372', 'vk6.49947', 'vk6.49968', 'vk6.49982', 'vk6.53994', 'vk6.54014', 'vk6.54048', 'vk6.54494'] |
| 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 | O1O2O3O4U2O5U4U6U5O6U1U3 |
| R3 orbit | {'O1O2O3O4U2O5U4U6U5O6U1U3'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U2U4O5U6U5U1O6U3 |
| Gauss code of K* | O1O2O3U2O4O5U4U6U5U1O6U3 |
| Gauss code of -K* | O1O2O3U1O4U3U5U4U6O5O6U2 |
| 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 -1 -2 2 0 2 -1],[ 1 0 -1 2 0 2 0],[ 2 1 0 2 1 1 2],[-2 -2 -2 0 -1 2 -3],[ 0 0 -1 1 0 1 -1],[-2 -2 -1 -2 -1 0 -2],[ 1 0 -2 3 1 2 0]] |
| Primitive based matrix | [[ 0 2 2 0 -1 -1 -2],[-2 0 2 -1 -2 -3 -2],[-2 -2 0 -1 -2 -2 -1],[ 0 1 1 0 0 -1 -1],[ 1 2 2 0 0 0 -1],[ 1 3 2 1 0 0 -2],[ 2 2 1 1 1 2 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-2,0,1,1,2,-2,1,2,3,2,1,2,2,1,0,1,1,0,1,2] |
| Phi over symmetry | [-2,-2,0,1,1,2,-2,1,1,1,3,1,0,1,2,0,1,1,0,-1,0] |
| Phi of -K | [-2,-1,-1,0,2,2,-1,0,1,2,3,0,0,0,1,1,1,1,1,1,-2] |
| Phi of K* | [-2,-2,0,1,1,2,-2,1,1,1,3,1,0,1,2,0,1,1,0,-1,0] |
| Phi of -K* | [-2,-1,-1,0,2,2,1,2,1,1,2,0,0,2,2,1,2,3,1,1,-2] |
| Symmetry type of based matrix | c |
| u-polynomial | -t^2+2t |
| Normalized Jones-Krushkal polynomial | 17z+35 |
| Enhanced Jones-Krushkal polynomial | 17w^2z+35w |
| Inner characteristic polynomial | t^6+39t^4+33t^2+1 |
| Outer characteristic polynomial | t^7+53t^5+52t^3+5t |
| Flat arrow polynomial | -10*K1**2 - 4*K1*K2 + 2*K1 + 5*K2 + 2*K3 + 6 |
| 2-strand cable arrow polynomial | -64*K1**4*K2**2 + 384*K1**4*K2 - 1792*K1**4 + 160*K1**3*K2*K3 - 800*K1**3*K3 + 64*K1**2*K2**3 - 2000*K1**2*K2**2 + 192*K1**2*K2*K3**2 - 160*K1**2*K2*K4 + 6448*K1**2*K2 - 608*K1**2*K3**2 - 32*K1**2*K3*K5 - 5136*K1**2 - 576*K1*K2**2*K3 - 32*K1*K2**2*K5 - 192*K1*K2*K3*K4 + 5056*K1*K2*K3 + 872*K1*K3*K4 + 96*K1*K4*K5 - 136*K2**4 - 208*K2**2*K3**2 - 48*K2**2*K4**2 + 600*K2**2*K4 - 3900*K2**2 + 256*K2*K3*K5 + 32*K2*K4*K6 - 1844*K3**2 - 406*K4**2 - 84*K5**2 - 4*K6**2 + 3860 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {3, 5}, {2, 4}], [{1, 6}, {3, 5}, {4}, {2}]] |
| If K is slice | False |