| Min(phi) over symmetries of the knot is: [-3,-1,0,1,1,2,0,2,3,3,2,1,1,1,0,0,1,1,0,2,1] |
| Flat knots (up to 7 crossings) with same phi are :['6.1087'] |
| 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+46t^5+41t^3+7t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1087'] |
| 2-strand cable arrow polynomial of the knot is: -192*K1**6 - 192*K1**4*K2**2 + 1088*K1**4*K2 - 3536*K1**4 + 608*K1**3*K2*K3 + 64*K1**3*K3*K4 - 480*K1**3*K3 + 704*K1**2*K2**3 - 4512*K1**2*K2**2 - 544*K1**2*K2*K4 + 7184*K1**2*K2 - 784*K1**2*K3**2 - 272*K1**2*K4**2 - 3376*K1**2 - 832*K1*K2**2*K3 - 256*K1*K2*K3*K4 + 5240*K1*K2*K3 + 1416*K1*K3*K4 + 264*K1*K4*K5 - 392*K2**4 - 16*K2**2*K3**2 - 8*K2**2*K4**2 + 808*K2**2*K4 - 3206*K2**2 + 104*K2*K3*K5 + 8*K2*K4*K6 - 1624*K3**2 - 582*K4**2 - 56*K5**2 - 2*K6**2 + 3372 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1087'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.13883', 'vk6.13980', 'vk6.14118', 'vk6.14341', 'vk6.14958', 'vk6.15081', 'vk6.15572', 'vk6.16044', 'vk6.16291', 'vk6.16316', 'vk6.17413', 'vk6.22606', 'vk6.22639', 'vk6.23921', 'vk6.33694', 'vk6.33771', 'vk6.34133', 'vk6.34258', 'vk6.34592', 'vk6.36198', 'vk6.36225', 'vk6.42291', 'vk6.53869', 'vk6.53912', 'vk6.54093', 'vk6.54418', 'vk6.54588', 'vk6.55572', 'vk6.59035', 'vk6.59066', 'vk6.60063', 'vk6.64553'] |
| 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 | O1O2O3O4U1U3O5U2U5O6U4U6 |
| R3 orbit | {'O1O2O3O4U1U3O5U2U5O6U4U6'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U5U1O5U6U3O6U2U4 |
| Gauss code of K* | O1O2U3O4O3U5O6O5U1U4U2U6 |
| Gauss code of -K* | O1O2U1O3O4U3O5O6U2U5U4U6 |
| 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 0 2 1 1],[ 3 0 2 1 3 1 1],[ 1 -2 0 0 3 1 1],[ 0 -1 0 0 1 0 1],[-2 -3 -3 -1 0 0 1],[-1 -1 -1 0 0 0 0],[-1 -1 -1 -1 -1 0 0]] |
| Primitive based matrix | [[ 0 2 1 1 0 -1 -3],[-2 0 1 0 -1 -3 -3],[-1 -1 0 0 -1 -1 -1],[-1 0 0 0 0 -1 -1],[ 0 1 1 0 0 0 -1],[ 1 3 1 1 0 0 -2],[ 3 3 1 1 1 2 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,-1,0,1,3,-1,0,1,3,3,0,1,1,1,0,1,1,0,1,2] |
| Phi over symmetry | [-3,-1,0,1,1,2,0,2,3,3,2,1,1,1,0,0,1,1,0,2,1] |
| Phi of -K | [-3,-1,0,1,1,2,0,2,3,3,2,1,1,1,0,0,1,1,0,2,1] |
| Phi of K* | [-2,-1,-1,0,1,3,1,2,1,0,2,0,1,1,3,0,1,3,1,2,0] |
| Phi of -K* | [-3,-1,0,1,1,2,2,1,1,1,3,0,1,1,3,0,1,1,0,0,-1] |
| Symmetry type of based matrix | c |
| u-polynomial | t^3-t^2-t |
| Normalized Jones-Krushkal polynomial | 4z^2+25z+35 |
| Enhanced Jones-Krushkal polynomial | 4w^3z^2+25w^2z+35w |
| Inner characteristic polynomial | t^6+30t^4+18t^2+1 |
| Outer characteristic polynomial | t^7+46t^5+41t^3+7t |
| Flat arrow polynomial | -6*K1**2 - 2*K1*K2 + K1 + 3*K2 + K3 + 4 |
| 2-strand cable arrow polynomial | -192*K1**6 - 192*K1**4*K2**2 + 1088*K1**4*K2 - 3536*K1**4 + 608*K1**3*K2*K3 + 64*K1**3*K3*K4 - 480*K1**3*K3 + 704*K1**2*K2**3 - 4512*K1**2*K2**2 - 544*K1**2*K2*K4 + 7184*K1**2*K2 - 784*K1**2*K3**2 - 272*K1**2*K4**2 - 3376*K1**2 - 832*K1*K2**2*K3 - 256*K1*K2*K3*K4 + 5240*K1*K2*K3 + 1416*K1*K3*K4 + 264*K1*K4*K5 - 392*K2**4 - 16*K2**2*K3**2 - 8*K2**2*K4**2 + 808*K2**2*K4 - 3206*K2**2 + 104*K2*K3*K5 + 8*K2*K4*K6 - 1624*K3**2 - 582*K4**2 - 56*K5**2 - 2*K6**2 + 3372 |
| 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 |