| Min(phi) over symmetries of the knot is: [-3,-2,0,1,2,2,-1,2,2,2,4,1,1,1,2,0,1,1,1,0,-2] |
| Flat knots (up to 7 crossings) with same phi are :['6.816'] |
| 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+67t^5+38t^3+5t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.816'] |
| 2-strand cable arrow polynomial of the knot is: -64*K1**4*K2**2 + 192*K1**4*K2 - 352*K1**4 + 64*K1**3*K2*K3 - 224*K1**3*K3 + 352*K1**2*K2**3 - 3536*K1**2*K2**2 - 256*K1**2*K2*K4 + 4928*K1**2*K2 - 64*K1**2*K3**2 - 4140*K1**2 + 160*K1*K2**3*K3 - 320*K1*K2**2*K3 - 32*K1*K2*K3*K4 + 4224*K1*K2*K3 + 376*K1*K3*K4 + 72*K1*K4*K5 - 888*K2**4 - 160*K2**2*K3**2 - 8*K2**2*K4**2 + 848*K2**2*K4 - 2518*K2**2 + 112*K2*K3*K5 + 8*K2*K4*K6 - 1268*K3**2 - 326*K4**2 - 64*K5**2 - 2*K6**2 + 2884 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.816'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.71476', 'vk6.71503', 'vk6.71535', 'vk6.71562', 'vk6.72010', 'vk6.72029', 'vk6.72061', 'vk6.72081', 'vk6.72537', 'vk6.72546', 'vk6.72639', 'vk6.72664', 'vk6.72927', 'vk6.72964', 'vk6.73111', 'vk6.73138', 'vk6.73642', 'vk6.73677', 'vk6.73694', 'vk6.77105', 'vk6.77121', 'vk6.77157', 'vk6.77176', 'vk6.77450', 'vk6.77467', 'vk6.77945', 'vk6.77960', 'vk6.78581', 'vk6.81436', 'vk6.86903', 'vk6.87258', 'vk6.89346'] |
| 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 | O1O2O3O4U1O5U4U6U5U2O6U3 |
| R3 orbit | {'O1O2O3O4U1O5U4U6U5U2O6U3'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U2O5U3U6U5U1O6U4 |
| Gauss code of K* | O1O2O3O4U2O5U6U4U5U1O6U3 |
| Gauss code of -K* | O1O2O3O4U2O5U4U6U1U5O6U3 |
| 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 -3 1 2 0 2 -2],[ 3 0 2 3 1 1 2],[-1 -2 0 0 -1 1 -2],[-2 -3 0 0 -1 2 -3],[ 0 -1 1 1 0 1 -1],[-2 -1 -1 -2 -1 0 -2],[ 2 -2 2 3 1 2 0]] |
| Primitive based matrix | [[ 0 2 2 1 0 -2 -3],[-2 0 2 0 -1 -3 -3],[-2 -2 0 -1 -1 -2 -1],[-1 0 1 0 -1 -2 -2],[ 0 1 1 1 0 -1 -1],[ 2 3 2 2 1 0 -2],[ 3 3 1 2 1 2 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-2,-1,0,2,3,-2,0,1,3,3,1,1,2,1,1,2,2,1,1,2] |
| Phi over symmetry | [-3,-2,0,1,2,2,-1,2,2,2,4,1,1,1,2,0,1,1,1,0,-2] |
| Phi of -K | [-3,-2,0,1,2,2,-1,2,2,2,4,1,1,1,2,0,1,1,1,0,-2] |
| Phi of K* | [-2,-2,-1,0,2,3,-2,0,1,2,4,1,1,1,2,0,1,2,1,2,-1] |
| Phi of -K* | [-3,-2,0,1,2,2,2,1,2,1,3,1,2,2,3,1,1,1,1,0,-2] |
| Symmetry type of based matrix | c |
| u-polynomial | t^3-t^2-t |
| Normalized Jones-Krushkal polynomial | 5z^2+22z+25 |
| Enhanced Jones-Krushkal polynomial | 5w^3z^2+22w^2z+25w |
| Inner characteristic polynomial | t^6+45t^4+17t^2+1 |
| Outer characteristic polynomial | t^7+67t^5+38t^3+5t |
| Flat arrow polynomial | -6*K1**2 - 2*K1*K2 + K1 + 3*K2 + K3 + 4 |
| 2-strand cable arrow polynomial | -64*K1**4*K2**2 + 192*K1**4*K2 - 352*K1**4 + 64*K1**3*K2*K3 - 224*K1**3*K3 + 352*K1**2*K2**3 - 3536*K1**2*K2**2 - 256*K1**2*K2*K4 + 4928*K1**2*K2 - 64*K1**2*K3**2 - 4140*K1**2 + 160*K1*K2**3*K3 - 320*K1*K2**2*K3 - 32*K1*K2*K3*K4 + 4224*K1*K2*K3 + 376*K1*K3*K4 + 72*K1*K4*K5 - 888*K2**4 - 160*K2**2*K3**2 - 8*K2**2*K4**2 + 848*K2**2*K4 - 2518*K2**2 + 112*K2*K3*K5 + 8*K2*K4*K6 - 1268*K3**2 - 326*K4**2 - 64*K5**2 - 2*K6**2 + 2884 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {3, 5}, {2, 4}], [{1, 6}, {4, 5}, {2, 3}], [{2, 6}, {1, 5}, {3, 4}]] |
| If K is slice | False |