| Min(phi) over symmetries of the knot is: [-3,-2,1,1,1,2,0,1,2,2,4,0,1,1,2,-1,-1,-1,-1,0,1] |
| Flat knots (up to 7 crossings) with same phi are :['6.653'] |
| Arrow polynomial of the knot is: 12*K1**3 - 4*K1**2 - 10*K1*K2 - 4*K1 + 2*K2 + 2*K3 + 3 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.653', '6.1267'] |
| Outer characteristic polynomial of the knot is: t^7+56t^5+69t^3+10t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.653'] |
| 2-strand cable arrow polynomial of the knot is: -96*K1**4 - 64*K1**3*K3 - 576*K1**2*K2**4 + 1024*K1**2*K2**3 + 128*K1**2*K2**2*K4 - 8080*K1**2*K2**2 - 608*K1**2*K2*K4 + 8280*K1**2*K2 - 32*K1**2*K3**2 - 96*K1**2*K4**2 - 6304*K1**2 + 1824*K1*K2**3*K3 - 1600*K1*K2**2*K3 - 640*K1*K2**2*K5 - 128*K1*K2*K3*K4 + 8728*K1*K2*K3 + 880*K1*K3*K4 + 136*K1*K4*K5 - 352*K2**6 + 608*K2**4*K4 - 3216*K2**4 - 128*K2**3*K6 - 944*K2**2*K3**2 - 264*K2**2*K4**2 + 3408*K2**2*K4 - 4020*K2**2 + 480*K2*K3*K5 + 112*K2*K4*K6 - 2248*K3**2 - 924*K4**2 - 64*K5**2 - 12*K6**2 + 4786 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.653'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.11059', 'vk6.11137', 'vk6.12223', 'vk6.12330', 'vk6.18339', 'vk6.18678', 'vk6.24779', 'vk6.25238', 'vk6.30636', 'vk6.30731', 'vk6.31870', 'vk6.31940', 'vk6.36965', 'vk6.37424', 'vk6.44154', 'vk6.44476', 'vk6.51860', 'vk6.51905', 'vk6.52725', 'vk6.52832', 'vk6.56115', 'vk6.56338', 'vk6.60634', 'vk6.60971', 'vk6.63522', 'vk6.63567', 'vk6.64002', 'vk6.64047', 'vk6.65767', 'vk6.66030', 'vk6.68774', 'vk6.68984'] |
| 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 | O1O2O3O4U2O5U1U4O6U5U6U3 |
| R3 orbit | {'O1O2O3O4U2O5U1U4O6U5U6U3'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U2U5U6O5U1U4O6U3 |
| Gauss code of K* | O1O2O3U4U5U3U6O5U1O4O6U2 |
| Gauss code of -K* | O1O2O3U2O4O5U3O6U4U1U6U5 |
| 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 -2 2 1 1 1],[ 3 0 0 4 2 2 1],[ 2 0 0 2 1 1 0],[-2 -4 -2 0 -1 0 1],[-1 -2 -1 1 0 1 1],[-1 -2 -1 0 -1 0 1],[-1 -1 0 -1 -1 -1 0]] |
| Primitive based matrix | [[ 0 2 1 1 1 -2 -3],[-2 0 1 0 -1 -2 -4],[-1 -1 0 -1 -1 0 -1],[-1 0 1 0 -1 -1 -2],[-1 1 1 1 0 -1 -2],[ 2 2 0 1 1 0 0],[ 3 4 1 2 2 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,-1,-1,2,3,-1,0,1,2,4,1,1,0,1,1,1,2,1,2,0] |
| Phi over symmetry | [-3,-2,1,1,1,2,0,1,2,2,4,0,1,1,2,-1,-1,-1,-1,0,1] |
| Phi of -K | [-3,-2,1,1,1,2,1,2,2,3,1,2,2,3,2,-1,-1,0,-1,1,2] |
| Phi of K* | [-2,-1,-1,-1,2,3,0,1,2,2,1,1,1,2,2,1,2,2,3,3,1] |
| Phi of -K* | [-3,-2,1,1,1,2,0,1,2,2,4,0,1,1,2,-1,-1,-1,-1,0,1] |
| Symmetry type of based matrix | c |
| u-polynomial | t^3-3t |
| Normalized Jones-Krushkal polynomial | 7z^2+26z+25 |
| Enhanced Jones-Krushkal polynomial | 7w^3z^2-2w^3z+28w^2z+25w |
| Inner characteristic polynomial | t^6+36t^4+19t^2+1 |
| Outer characteristic polynomial | t^7+56t^5+69t^3+10t |
| Flat arrow polynomial | 12*K1**3 - 4*K1**2 - 10*K1*K2 - 4*K1 + 2*K2 + 2*K3 + 3 |
| 2-strand cable arrow polynomial | -96*K1**4 - 64*K1**3*K3 - 576*K1**2*K2**4 + 1024*K1**2*K2**3 + 128*K1**2*K2**2*K4 - 8080*K1**2*K2**2 - 608*K1**2*K2*K4 + 8280*K1**2*K2 - 32*K1**2*K3**2 - 96*K1**2*K4**2 - 6304*K1**2 + 1824*K1*K2**3*K3 - 1600*K1*K2**2*K3 - 640*K1*K2**2*K5 - 128*K1*K2*K3*K4 + 8728*K1*K2*K3 + 880*K1*K3*K4 + 136*K1*K4*K5 - 352*K2**6 + 608*K2**4*K4 - 3216*K2**4 - 128*K2**3*K6 - 944*K2**2*K3**2 - 264*K2**2*K4**2 + 3408*K2**2*K4 - 4020*K2**2 + 480*K2*K3*K5 + 112*K2*K4*K6 - 2248*K3**2 - 924*K4**2 - 64*K5**2 - 12*K6**2 + 4786 |
| 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}], [{2, 6}, {5}, {4}, {3}, {1}], [{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}], [{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}], [{5, 6}, {4}, {3}, {2}, {1}], [{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}, {4, 5}, {3}, {2}, {1}], [{6}, {5}, {1, 4}, {2, 3}], [{6}, {5}, {2, 4}, {1, 3}], [{6}, {5}, {2, 4}, {3}, {1}], [{6}, {5}, {3, 4}, {1, 2}]] |
| If K is slice | False |