| Min(phi) over symmetries of the knot is: [-3,-1,0,1,1,2,1,1,1,3,2,0,1,2,2,0,0,1,0,0,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.627'] |
| Arrow polynomial of the knot is: 8*K1**3 - 10*K1**2 - 6*K1*K2 - 3*K1 + 5*K2 + K3 + 6 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.576', '6.581', '6.622', '6.627', '6.983', '6.1017'] |
| Outer characteristic polynomial of the knot is: t^7+48t^5+90t^3+7t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.627'] |
| 2-strand cable arrow polynomial of the knot is: -64*K1**6 + 2144*K1**4*K2 - 4560*K1**4 + 576*K1**3*K2*K3 - 1280*K1**3*K3 + 960*K1**2*K2**3 - 7008*K1**2*K2**2 + 64*K1**2*K2*K3**2 - 448*K1**2*K2*K4 + 11704*K1**2*K2 - 592*K1**2*K3**2 - 32*K1**2*K3*K5 - 80*K1**2*K4**2 - 6596*K1**2 + 416*K1*K2**3*K3 - 1920*K1*K2**2*K3 - 288*K1*K2**2*K5 - 64*K1*K2*K3*K4 + 7936*K1*K2*K3 - 32*K1*K2*K4*K5 + 1392*K1*K3*K4 + 160*K1*K4*K5 + 8*K1*K5*K6 - 64*K2**6 + 96*K2**4*K4 - 1352*K2**4 - 32*K2**3*K6 - 352*K2**2*K3**2 - 40*K2**2*K4**2 + 1784*K2**2*K4 - 5170*K2**2 + 352*K2*K3*K5 + 40*K2*K4*K6 - 2288*K3**2 - 698*K4**2 - 108*K5**2 - 6*K6**2 + 5440 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.627'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.11527', 'vk6.11858', 'vk6.12877', 'vk6.13184', 'vk6.20362', 'vk6.21704', 'vk6.27665', 'vk6.29210', 'vk6.31298', 'vk6.31693', 'vk6.32456', 'vk6.32871', 'vk6.39097', 'vk6.41351', 'vk6.45853', 'vk6.47515', 'vk6.52298', 'vk6.52562', 'vk6.53142', 'vk6.53446', 'vk6.57221', 'vk6.58443', 'vk6.61834', 'vk6.62967', 'vk6.63803', 'vk6.63935', 'vk6.64249', 'vk6.64445', 'vk6.66828', 'vk6.67697', 'vk6.69467', 'vk6.70190'] |
| 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 | O1O2O3O4U5O6U3O5U1U6U4U2 |
| R3 orbit | {'O1O2O3O4U5O6U3O5U1U6U4U2'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U3U1U5U4O6U2O5U6 |
| Gauss code of K* | O1O2O3O4U1U4U5U3O6U2O5U6 |
| Gauss code of -K* | O1O2O3O4U5O6U3O5U2U6U1U4 |
| 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 -1 2 0 1],[ 3 0 3 1 3 2 1],[-1 -3 0 -1 1 -1 0],[ 1 -1 1 0 1 1 0],[-2 -3 -1 -1 0 -1 -1],[ 0 -2 1 -1 1 0 1],[-1 -1 0 0 1 -1 0]] |
| Primitive based matrix | [[ 0 2 1 1 0 -1 -3],[-2 0 -1 -1 -1 -1 -3],[-1 1 0 0 -1 0 -1],[-1 1 0 0 -1 -1 -3],[ 0 1 1 1 0 -1 -2],[ 1 1 0 1 1 0 -1],[ 3 3 1 3 2 1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,-1,0,1,3,1,1,1,1,3,0,1,0,1,1,1,3,1,2,1] |
| Phi over symmetry | [-3,-1,0,1,1,2,1,1,1,3,2,0,1,2,2,0,0,1,0,0,0] |
| Phi of -K | [-3,-1,0,1,1,2,1,1,1,3,2,0,1,2,2,0,0,1,0,0,0] |
| Phi of K* | [-2,-1,-1,0,1,3,0,0,1,2,2,0,0,1,1,0,2,3,0,1,1] |
| Phi of -K* | [-3,-1,0,1,1,2,1,2,1,3,3,1,0,1,1,1,1,1,0,1,1] |
| 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+32t^4+49t^2 |
| Outer characteristic polynomial | t^7+48t^5+90t^3+7t |
| Flat arrow polynomial | 8*K1**3 - 10*K1**2 - 6*K1*K2 - 3*K1 + 5*K2 + K3 + 6 |
| 2-strand cable arrow polynomial | -64*K1**6 + 2144*K1**4*K2 - 4560*K1**4 + 576*K1**3*K2*K3 - 1280*K1**3*K3 + 960*K1**2*K2**3 - 7008*K1**2*K2**2 + 64*K1**2*K2*K3**2 - 448*K1**2*K2*K4 + 11704*K1**2*K2 - 592*K1**2*K3**2 - 32*K1**2*K3*K5 - 80*K1**2*K4**2 - 6596*K1**2 + 416*K1*K2**3*K3 - 1920*K1*K2**2*K3 - 288*K1*K2**2*K5 - 64*K1*K2*K3*K4 + 7936*K1*K2*K3 - 32*K1*K2*K4*K5 + 1392*K1*K3*K4 + 160*K1*K4*K5 + 8*K1*K5*K6 - 64*K2**6 + 96*K2**4*K4 - 1352*K2**4 - 32*K2**3*K6 - 352*K2**2*K3**2 - 40*K2**2*K4**2 + 1784*K2**2*K4 - 5170*K2**2 + 352*K2*K3*K5 + 40*K2*K4*K6 - 2288*K3**2 - 698*K4**2 - 108*K5**2 - 6*K6**2 + 5440 |
| 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}], [{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}, {2, 5}, {4}, {3}, {1}], [{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}, {1, 4}, {3}, {2}], [{6}, {5}, {2, 4}, {1, 3}], [{6}, {5}, {3, 4}, {1, 2}]] |
| If K is slice | False |