| Min(phi) over symmetries of the knot is: [-4,0,0,1,1,2,0,1,3,4,4,0,1,1,0,1,1,1,0,1,1] |
| Flat knots (up to 7 crossings) with same phi are :['6.500'] |
| Arrow polynomial of the knot is: 4*K1**2*K2 - 2*K1*K3 - K2 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.64', '6.74', '6.106', '6.178', '6.300', '6.397', '6.479', '6.481', '6.500'] |
| Outer characteristic polynomial of the knot is: t^7+61t^5+98t^3+13t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.500'] |
| 2-strand cable arrow polynomial of the knot is: -256*K1**4 + 128*K1**3*K2*K3 + 480*K1**2*K2**3 + 128*K1**2*K2**2*K4 - 2656*K1**2*K2**2 - 512*K1**2*K2*K4 + 3320*K1**2*K2 - 576*K1**2*K3**2 - 32*K1**2*K4**2 - 3528*K1**2 + 128*K1*K2**3*K3 + 96*K1*K2**2*K3*K4 - 544*K1*K2**2*K3 + 128*K1*K2**2*K4*K5 - 640*K1*K2**2*K5 - 640*K1*K2*K3*K4 + 4664*K1*K2*K3 - 64*K1*K2*K4*K5 + 1440*K1*K3*K4 + 640*K1*K4*K5 + 16*K1*K5*K6 - 32*K2**4*K4**2 + 256*K2**4*K4 - 1344*K2**4 + 32*K2**3*K3*K5 + 32*K2**3*K4*K6 - 64*K2**3*K6 - 416*K2**2*K3**2 - 496*K2**2*K4**2 + 2184*K2**2*K4 - 160*K2**2*K5**2 - 8*K2**2*K6**2 - 2968*K2**2 - 32*K2*K3*K4*K5 + 1384*K2*K3*K5 + 224*K2*K4*K6 + 56*K2*K5*K7 - 1984*K3**2 - 1154*K4**2 - 600*K5**2 - 24*K6**2 + 3392 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.500'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.17130', 'vk6.17373', 'vk6.20606', 'vk6.22020', 'vk6.23535', 'vk6.23869', 'vk6.28076', 'vk6.29527', 'vk6.35699', 'vk6.36122', 'vk6.39486', 'vk6.41693', 'vk6.43038', 'vk6.43344', 'vk6.46079', 'vk6.47738', 'vk6.55279', 'vk6.55527', 'vk6.57478', 'vk6.58642', 'vk6.59703', 'vk6.60043', 'vk6.62153', 'vk6.63111', 'vk6.65084', 'vk6.65272', 'vk6.67006', 'vk6.67873', 'vk6.68334', 'vk6.68482', 'vk6.69626', 'vk6.70314'] |
| 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 | O1O2O3O4O5U1U5U4O6U3U2U6 |
| R3 orbit | {'O1O2O3O4O5U1U5U4O6U3U2U6'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4O5U6U4U3O6U2U1U5 |
| Gauss code of K* | O1O2O3U4O5O6O4U1U6U5U3U2 |
| Gauss code of -K* | O1O2O3U1O4O5O6U5U4U3U2U6 |
| 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 -4 0 0 1 1 2],[ 4 0 4 3 2 1 2],[ 0 -4 0 0 0 0 2],[ 0 -3 0 0 0 0 1],[-1 -2 0 0 0 0 0],[-1 -1 0 0 0 0 0],[-2 -2 -2 -1 0 0 0]] |
| Primitive based matrix | [[ 0 2 1 1 0 0 -4],[-2 0 0 0 -1 -2 -2],[-1 0 0 0 0 0 -1],[-1 0 0 0 0 0 -2],[ 0 1 0 0 0 0 -3],[ 0 2 0 0 0 0 -4],[ 4 2 1 2 3 4 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,-1,0,0,4,0,0,1,2,2,0,0,0,1,0,0,2,0,3,4] |
| Phi over symmetry | [-4,0,0,1,1,2,0,1,3,4,4,0,1,1,0,1,1,1,0,1,1] |
| Phi of -K | [-4,0,0,1,1,2,0,1,3,4,4,0,1,1,0,1,1,1,0,1,1] |
| Phi of K* | [-2,-1,-1,0,0,4,1,1,0,1,4,0,1,1,3,1,1,4,0,0,1] |
| Phi of -K* | [-4,0,0,1,1,2,3,4,1,2,2,0,0,0,1,0,0,2,0,0,0] |
| Symmetry type of based matrix | c |
| u-polynomial | t^4-t^2-2t |
| Normalized Jones-Krushkal polynomial | 9z^2+30z+25 |
| Enhanced Jones-Krushkal polynomial | 9w^3z^2+30w^2z+25w |
| Inner characteristic polynomial | t^6+39t^4+29t^2 |
| Outer characteristic polynomial | t^7+61t^5+98t^3+13t |
| Flat arrow polynomial | 4*K1**2*K2 - 2*K1*K3 - K2 |
| 2-strand cable arrow polynomial | -256*K1**4 + 128*K1**3*K2*K3 + 480*K1**2*K2**3 + 128*K1**2*K2**2*K4 - 2656*K1**2*K2**2 - 512*K1**2*K2*K4 + 3320*K1**2*K2 - 576*K1**2*K3**2 - 32*K1**2*K4**2 - 3528*K1**2 + 128*K1*K2**3*K3 + 96*K1*K2**2*K3*K4 - 544*K1*K2**2*K3 + 128*K1*K2**2*K4*K5 - 640*K1*K2**2*K5 - 640*K1*K2*K3*K4 + 4664*K1*K2*K3 - 64*K1*K2*K4*K5 + 1440*K1*K3*K4 + 640*K1*K4*K5 + 16*K1*K5*K6 - 32*K2**4*K4**2 + 256*K2**4*K4 - 1344*K2**4 + 32*K2**3*K3*K5 + 32*K2**3*K4*K6 - 64*K2**3*K6 - 416*K2**2*K3**2 - 496*K2**2*K4**2 + 2184*K2**2*K4 - 160*K2**2*K5**2 - 8*K2**2*K6**2 - 2968*K2**2 - 32*K2*K3*K4*K5 + 1384*K2*K3*K5 + 224*K2*K4*K6 + 56*K2*K5*K7 - 1984*K3**2 - 1154*K4**2 - 600*K5**2 - 24*K6**2 + 3392 |
| 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 |