| Min(phi) over symmetries of the knot is: [-3,-1,0,1,1,2,1,1,1,2,4,0,0,0,2,0,-1,0,-1,-1,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.972'] |
| 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+60t^5+67t^3+9t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.972'] |
| 2-strand cable arrow polynomial of the knot is: -192*K1**4*K2**2 + 288*K1**4*K2 - 496*K1**4 + 128*K1**3*K2*K3 - 256*K1**3*K3 + 896*K1**2*K2**3 - 4880*K1**2*K2**2 - 256*K1**2*K2*K4 + 5984*K1**2*K2 - 80*K1**2*K3**2 - 4720*K1**2 + 352*K1*K2**3*K3 - 736*K1*K2**2*K3 - 64*K1*K2**2*K5 + 5384*K1*K2*K3 + 336*K1*K3*K4 + 16*K1*K4*K5 - 1768*K2**4 - 336*K2**2*K3**2 - 8*K2**2*K4**2 + 1400*K2**2*K4 - 2662*K2**2 + 168*K2*K3*K5 + 8*K2*K4*K6 - 1500*K3**2 - 310*K4**2 - 36*K5**2 - 2*K6**2 + 3340 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.972'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.71563', 'vk6.71670', 'vk6.72086', 'vk6.72303', 'vk6.74036', 'vk6.74599', 'vk6.76084', 'vk6.76796', 'vk6.77183', 'vk6.77282', 'vk6.77480', 'vk6.77646', 'vk6.79028', 'vk6.79606', 'vk6.80563', 'vk6.81015', 'vk6.81104', 'vk6.81138', 'vk6.81161', 'vk6.81215', 'vk6.81315', 'vk6.81462', 'vk6.82253', 'vk6.83507', 'vk6.83837', 'vk6.83971', 'vk6.85407', 'vk6.86326', 'vk6.87098', 'vk6.88031', 'vk6.88327', 'vk6.88962'] |
| 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 | O1O2O3O4U1U2O5U3O6U4U5U6 |
| R3 orbit | {'O1O2O3O4U1U2O5U3O6U4U5U6'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U5U6U1O5U2O6U3U4 |
| Gauss code of K* | O1O2O3U4U5U6U1O4O5U2O6U3 |
| Gauss code of -K* | O1O2O3U1O4U2O5O6U3U4U5U6 |
| 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 1 1 2],[ 3 0 1 2 3 2 1],[ 1 -1 0 1 2 2 1],[ 0 -2 -1 0 1 2 2],[-1 -3 -2 -1 0 1 2],[-1 -2 -2 -2 -1 0 1],[-2 -1 -1 -2 -2 -1 0]] |
| Primitive based matrix | [[ 0 2 1 1 0 -1 -3],[-2 0 -1 -2 -2 -1 -1],[-1 1 0 -1 -2 -2 -2],[-1 2 1 0 -1 -2 -3],[ 0 2 2 1 0 -1 -2],[ 1 1 2 2 1 0 -1],[ 3 1 2 3 2 1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,-1,0,1,3,1,2,2,1,1,1,2,2,2,1,2,3,1,2,1] |
| Phi over symmetry | [-3,-1,0,1,1,2,1,1,1,2,4,0,0,0,2,0,-1,0,-1,-1,0] |
| Phi of -K | [-3,-1,0,1,1,2,1,1,1,2,4,0,0,0,2,0,-1,0,-1,-1,0] |
| Phi of K* | [-2,-1,-1,0,1,3,-1,0,0,2,4,1,0,0,1,-1,0,2,0,1,1] |
| Phi of -K* | [-3,-1,0,1,1,2,1,2,2,3,1,1,2,2,1,2,1,2,-1,1,2] |
| Symmetry type of based matrix | c |
| u-polynomial | t^3-t^2-t |
| Normalized Jones-Krushkal polynomial | 6z^2+23z+23 |
| Enhanced Jones-Krushkal polynomial | -2w^4z^2+8w^3z^2-2w^3z+25w^2z+23w |
| Inner characteristic polynomial | t^6+44t^4+14t^2+1 |
| Outer characteristic polynomial | t^7+60t^5+67t^3+9t |
| Flat arrow polynomial | -6*K1**2 - 2*K1*K2 + K1 + 3*K2 + K3 + 4 |
| 2-strand cable arrow polynomial | -192*K1**4*K2**2 + 288*K1**4*K2 - 496*K1**4 + 128*K1**3*K2*K3 - 256*K1**3*K3 + 896*K1**2*K2**3 - 4880*K1**2*K2**2 - 256*K1**2*K2*K4 + 5984*K1**2*K2 - 80*K1**2*K3**2 - 4720*K1**2 + 352*K1*K2**3*K3 - 736*K1*K2**2*K3 - 64*K1*K2**2*K5 + 5384*K1*K2*K3 + 336*K1*K3*K4 + 16*K1*K4*K5 - 1768*K2**4 - 336*K2**2*K3**2 - 8*K2**2*K4**2 + 1400*K2**2*K4 - 2662*K2**2 + 168*K2*K3*K5 + 8*K2*K4*K6 - 1500*K3**2 - 310*K4**2 - 36*K5**2 - 2*K6**2 + 3340 |
| Genus of based matrix | 2 |
| Fillings of based matrix | [[{1, 6}, {2, 5}, {3, 4}], [{1, 6}, {2, 5}, {4}, {3}], [{1, 6}, {3, 5}, {2, 4}], [{1, 6}, {3, 5}, {4}, {2}], [{1, 6}, {4, 5}, {2, 3}], [{1, 6}, {4, 5}, {3}, {2}], [{1, 6}, {5}, {2, 4}, {3}], [{1, 6}, {5}, {3, 4}, {2}], [{1, 6}, {5}, {4}, {2, 3}], [{1, 6}, {5}, {4}, {3}, {2}], [{2, 6}, {1, 5}, {3, 4}], [{2, 6}, {1, 5}, {4}, {3}], [{2, 6}, {3, 5}, {1, 4}], [{2, 6}, {3, 5}, {4}, {1}], [{2, 6}, {4, 5}, {1, 3}], [{2, 6}, {4, 5}, {3}, {1}], [{2, 6}, {5}, {1, 4}, {3}], [{2, 6}, {5}, {3, 4}, {1}], [{2, 6}, {5}, {4}, {1, 3}], [{3, 6}, {1, 5}, {2, 4}], [{3, 6}, {1, 5}, {4}, {2}], [{3, 6}, {2, 5}, {1, 4}], [{3, 6}, {2, 5}, {4}, {1}], [{3, 6}, {4, 5}, {1, 2}], [{3, 6}, {4, 5}, {2}, {1}], [{3, 6}, {5}, {1, 4}, {2}], [{3, 6}, {5}, {2, 4}, {1}], [{3, 6}, {5}, {4}, {1, 2}], [{4, 6}, {1, 5}, {2, 3}], [{4, 6}, {1, 5}, {3}, {2}], [{4, 6}, {2, 5}, {1, 3}], [{4, 6}, {2, 5}, {3}, {1}], [{4, 6}, {3, 5}, {1, 2}], [{4, 6}, {3, 5}, {2}, {1}], [{4, 6}, {5}, {1, 3}, {2}], [{4, 6}, {5}, {2, 3}, {1}], [{4, 6}, {5}, {3}, {1, 2}], [{5, 6}, {1, 4}, {2, 3}], [{5, 6}, {1, 4}, {3}, {2}], [{5, 6}, {2, 4}, {1, 3}], [{5, 6}, {2, 4}, {3}, {1}], [{5, 6}, {3, 4}, {1, 2}], [{5, 6}, {3, 4}, {2}, {1}], [{5, 6}, {4}, {1, 3}, {2}], [{5, 6}, {4}, {2, 3}, {1}], [{5, 6}, {4}, {3}, {1, 2}], [{6}, {1, 5}, {2, 4}, {3}], [{6}, {1, 5}, {3, 4}, {2}], [{6}, {1, 5}, {4}, {2, 3}], [{6}, {2, 5}, {1, 4}, {3}], [{6}, {2, 5}, {3, 4}, {1}], [{6}, {2, 5}, {4}, {1, 3}], [{6}, {3, 5}, {1, 4}, {2}], [{6}, {3, 5}, {2, 4}, {1}], [{6}, {3, 5}, {4}, {1, 2}], [{6}, {3, 5}, {4}, {2}, {1}], [{6}, {4, 5}, {1, 3}, {2}], [{6}, {4, 5}, {2, 3}, {1}], [{6}, {4, 5}, {3}, {1, 2}], [{6}, {5}, {1, 4}, {2, 3}], [{6}, {5}, {2, 4}, {1, 3}], [{6}, {5}, {3, 4}, {1, 2}]] |
| If K is slice | False |