| Min(phi) over symmetries of the knot is: [-2,-1,0,1,1,1,-1,1,1,1,2,1,0,1,1,1,1,1,1,0,-1] |
| Flat knots (up to 7 crossings) with same phi are :['6.1522'] |
| 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+30t^5+32t^3+7t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1522'] |
| 2-strand cable arrow polynomial of the knot is: -448*K1**6 - 320*K1**4*K2**2 + 2016*K1**4*K2 - 5392*K1**4 + 480*K1**3*K2*K3 + 32*K1**3*K3*K4 - 800*K1**3*K3 + 1248*K1**2*K2**3 - 8080*K1**2*K2**2 - 704*K1**2*K2*K4 + 11440*K1**2*K2 - 752*K1**2*K3**2 - 176*K1**2*K4**2 - 4848*K1**2 - 1088*K1*K2**2*K3 - 288*K1*K2*K3*K4 + 8144*K1*K2*K3 + 1528*K1*K3*K4 + 232*K1*K4*K5 - 1608*K2**4 - 288*K2**2*K3**2 - 48*K2**2*K4**2 + 1872*K2**2*K4 - 4420*K2**2 + 384*K2*K3*K5 + 32*K2*K4*K6 - 2196*K3**2 - 818*K4**2 - 124*K5**2 - 4*K6**2 + 4992 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1522'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.11268', 'vk6.11346', 'vk6.12533', 'vk6.12644', 'vk6.17612', 'vk6.18922', 'vk6.18998', 'vk6.19346', 'vk6.19641', 'vk6.24071', 'vk6.24163', 'vk6.25520', 'vk6.25619', 'vk6.26118', 'vk6.26538', 'vk6.30950', 'vk6.31073', 'vk6.32130', 'vk6.32249', 'vk6.36415', 'vk6.37655', 'vk6.37702', 'vk6.43517', 'vk6.44771', 'vk6.52018', 'vk6.52109', 'vk6.52934', 'vk6.56501', 'vk6.56662', 'vk6.65383', 'vk6.66125', 'vk6.66159'] |
| 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 | O1O2O3U2O4U5U1O5O6U4U3U6 |
| R3 orbit | {'O1O2O3U2O4U5U1O5O6U4U3U6'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U4U1U5O4O6U3U6O5U2 |
| Gauss code of K* | O1O2O3U4U5U2O5U1O6O4U6U3 |
| Gauss code of -K* | O1O2O3U1U4O5O4U3O6U2U6U5 |
| 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 -1 1 0 -1 2],[ 1 0 0 2 0 1 2],[ 1 0 0 1 0 1 1],[-1 -2 -1 0 0 -1 2],[ 0 0 0 0 0 0 1],[ 1 -1 -1 1 0 0 2],[-2 -2 -1 -2 -1 -2 0]] |
| Primitive based matrix | [[ 0 2 1 0 -1 -1 -1],[-2 0 -2 -1 -1 -2 -2],[-1 2 0 0 -1 -1 -2],[ 0 1 0 0 0 0 0],[ 1 1 1 0 0 1 0],[ 1 2 1 0 -1 0 -1],[ 1 2 2 0 0 1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,0,1,1,1,2,1,1,2,2,0,1,1,2,0,0,0,-1,0,1] |
| Phi over symmetry | [-2,-1,0,1,1,1,-1,1,1,1,2,1,0,1,1,1,1,1,1,0,-1] |
| Phi of -K | [-1,-1,-1,0,1,2,-1,0,1,0,1,1,1,1,1,1,1,2,1,1,-1] |
| Phi of K* | [-2,-1,0,1,1,1,-1,1,1,1,2,1,0,1,1,1,1,1,1,0,-1] |
| Phi of -K* | [-1,-1,-1,0,1,2,-1,-1,0,1,2,0,0,1,1,0,2,2,0,1,2] |
| Symmetry type of based matrix | c |
| u-polynomial | -t^2+2t |
| Normalized Jones-Krushkal polynomial | 3z^2+24z+37 |
| Enhanced Jones-Krushkal polynomial | 3w^3z^2+24w^2z+37w |
| Inner characteristic polynomial | t^6+22t^4+11t^2+1 |
| Outer characteristic polynomial | t^7+30t^5+32t^3+7t |
| Flat arrow polynomial | -10*K1**2 - 4*K1*K2 + 2*K1 + 5*K2 + 2*K3 + 6 |
| 2-strand cable arrow polynomial | -448*K1**6 - 320*K1**4*K2**2 + 2016*K1**4*K2 - 5392*K1**4 + 480*K1**3*K2*K3 + 32*K1**3*K3*K4 - 800*K1**3*K3 + 1248*K1**2*K2**3 - 8080*K1**2*K2**2 - 704*K1**2*K2*K4 + 11440*K1**2*K2 - 752*K1**2*K3**2 - 176*K1**2*K4**2 - 4848*K1**2 - 1088*K1*K2**2*K3 - 288*K1*K2*K3*K4 + 8144*K1*K2*K3 + 1528*K1*K3*K4 + 232*K1*K4*K5 - 1608*K2**4 - 288*K2**2*K3**2 - 48*K2**2*K4**2 + 1872*K2**2*K4 - 4420*K2**2 + 384*K2*K3*K5 + 32*K2*K4*K6 - 2196*K3**2 - 818*K4**2 - 124*K5**2 - 4*K6**2 + 4992 |
| 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}], [{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}], [{3, 6}, {5}, {4}, {2}, {1}], [{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}], [{4, 6}, {5}, {3}, {2}, {1}], [{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}, {1, 5}, {4}, {3}, {2}], [{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}, {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}], [{6}, {5}, {3, 4}, {2}, {1}]] |
| If K is slice | False |