| Min(phi) over symmetries of the knot is: [-3,-1,0,1,1,2,0,2,1,2,3,2,1,1,1,1,0,1,-1,0,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.785'] |
| Arrow polynomial of the knot is: -6*K1**2 - 2*K1*K2 + K1 + 3*K2 + K3 + 4 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.323', '6.380', '6.444', '6.472', '6.523', '6.579', '6.592', '6.595', '6.609', '6.614', '6.620', '6.644', '6.648', '6.669', '6.671', '6.681', '6.693', '6.724', '6.725', '6.757', '6.766', '6.785', '6.786', '6.797', '6.798', '6.816', '6.833', '6.972', '6.978', '6.1056', '6.1064', '6.1066', '6.1087', '6.1094', '6.1273', '6.1277', '6.1282', '6.1295', '6.1300', '6.1313', '6.1344', '6.1353', '6.1354'] |
| Outer characteristic polynomial of the knot is: t^7+44t^5+104t^3+16t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.785'] |
| 2-strand cable arrow polynomial of the knot is: -192*K1**4*K2**2 + 576*K1**4*K2 - 1440*K1**4 + 160*K1**3*K2*K3 - 352*K1**3*K3 + 384*K1**2*K2**3 - 3088*K1**2*K2**2 - 224*K1**2*K2*K4 + 6184*K1**2*K2 - 64*K1**2*K3**2 - 4888*K1**2 + 96*K1*K2**3*K3 - 736*K1*K2**2*K3 + 4720*K1*K2*K3 + 584*K1*K3*K4 + 32*K1*K4*K5 - 312*K2**4 - 176*K2**2*K3**2 - 8*K2**2*K4**2 + 728*K2**2*K4 - 3686*K2**2 + 120*K2*K3*K5 + 8*K2*K4*K6 - 1652*K3**2 - 406*K4**2 - 44*K5**2 - 2*K6**2 + 3676 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.785'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.11224', 'vk6.11303', 'vk6.12487', 'vk6.12598', 'vk6.18233', 'vk6.18568', 'vk6.24704', 'vk6.25117', 'vk6.30892', 'vk6.31015', 'vk6.32076', 'vk6.32195', 'vk6.36821', 'vk6.37282', 'vk6.44064', 'vk6.44403', 'vk6.51984', 'vk6.52079', 'vk6.52865', 'vk6.52912', 'vk6.56026', 'vk6.56300', 'vk6.60574', 'vk6.60912', 'vk6.63636', 'vk6.63681', 'vk6.64066', 'vk6.64111', 'vk6.65685', 'vk6.65975', 'vk6.68733', 'vk6.68941'] |
| 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 | O1O2O3O4U3O5U6U4U1O6U2U5 |
| R3 orbit | {'O1O2O3O4U3O5U6U4U1O6U2U5'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U5U3O6U4U1U6O5U2 |
| Gauss code of K* | O1O2O3U1O4O5U3U4U6U2O6U5 |
| Gauss code of -K* | O1O2O3U4O5U2U5U6U1O4O6U3 |
| 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 0 -1 1 3 -2],[ 1 0 0 -1 1 2 0],[ 0 0 0 -1 2 2 -1],[ 1 1 1 0 1 1 0],[-1 -1 -2 -1 0 0 -1],[-3 -2 -2 -1 0 0 -3],[ 2 0 1 0 1 3 0]] |
| Primitive based matrix | [[ 0 3 1 0 -1 -1 -2],[-3 0 0 -2 -1 -2 -3],[-1 0 0 -2 -1 -1 -1],[ 0 2 2 0 -1 0 -1],[ 1 1 1 1 0 1 0],[ 1 2 1 0 -1 0 0],[ 2 3 1 1 0 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-3,-1,0,1,1,2,0,2,1,2,3,2,1,1,1,1,0,1,-1,0,0] |
| Phi over symmetry | [-3,-1,0,1,1,2,0,2,1,2,3,2,1,1,1,1,0,1,-1,0,0] |
| Phi of -K | [-2,-1,-1,0,1,3,1,1,1,2,2,-1,0,1,3,1,1,2,-1,1,2] |
| Phi of K* | [-3,-1,0,1,1,2,2,1,2,3,2,-1,1,1,2,1,0,1,-1,1,1] |
| Phi of -K* | [-2,-1,-1,0,1,3,0,0,1,1,3,-1,0,1,2,1,1,1,2,2,0] |
| Symmetry type of based matrix | c |
| u-polynomial | -t^3+t^2+t |
| Normalized Jones-Krushkal polynomial | 2z^2+19z+31 |
| Enhanced Jones-Krushkal polynomial | 2w^3z^2-4w^3z+23w^2z+31w |
| Inner characteristic polynomial | t^6+28t^4+47t^2+4 |
| Outer characteristic polynomial | t^7+44t^5+104t^3+16t |
| Flat arrow polynomial | -6*K1**2 - 2*K1*K2 + K1 + 3*K2 + K3 + 4 |
| 2-strand cable arrow polynomial | -192*K1**4*K2**2 + 576*K1**4*K2 - 1440*K1**4 + 160*K1**3*K2*K3 - 352*K1**3*K3 + 384*K1**2*K2**3 - 3088*K1**2*K2**2 - 224*K1**2*K2*K4 + 6184*K1**2*K2 - 64*K1**2*K3**2 - 4888*K1**2 + 96*K1*K2**3*K3 - 736*K1*K2**2*K3 + 4720*K1*K2*K3 + 584*K1*K3*K4 + 32*K1*K4*K5 - 312*K2**4 - 176*K2**2*K3**2 - 8*K2**2*K4**2 + 728*K2**2*K4 - 3686*K2**2 + 120*K2*K3*K5 + 8*K2*K4*K6 - 1652*K3**2 - 406*K4**2 - 44*K5**2 - 2*K6**2 + 3676 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{3, 6}, {1, 5}, {2, 4}], [{5, 6}, {2, 4}, {1, 3}]] |
| If K is slice | False |