| Min(phi) over symmetries of the knot is: [-3,-2,0,1,2,2,-1,1,4,2,4,0,2,0,1,0,1,1,2,1,-1] |
| Flat knots (up to 7 crossings) with same phi are :['6.736'] |
| Arrow polynomial of the knot is: 4*K1**3 - 10*K1**2 - 2*K1*K2 - 2*K1 + 5*K2 + 6 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.618', '6.640', '6.736', '6.787'] |
| Outer characteristic polynomial of the knot is: t^7+75t^5+63t^3+9t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.736'] |
| 2-strand cable arrow polynomial of the knot is: 256*K1**4*K2**3 - 832*K1**4*K2**2 + 1024*K1**4*K2 - 1376*K1**4 + 192*K1**3*K2*K3 + 32*K1**3*K3*K4 - 64*K1**3*K3 - 832*K1**2*K2**4 + 3328*K1**2*K2**3 - 8320*K1**2*K2**2 - 640*K1**2*K2*K4 + 7976*K1**2*K2 - 128*K1**2*K3**2 - 32*K1**2*K4**2 - 5364*K1**2 + 672*K1*K2**3*K3 - 800*K1*K2**2*K3 - 96*K1*K2**2*K5 + 5792*K1*K2*K3 + 632*K1*K3*K4 + 24*K1*K4*K5 - 32*K2**6 + 32*K2**4*K4 - 1704*K2**4 - 176*K2**2*K3**2 - 8*K2**2*K4**2 + 904*K2**2*K4 - 2576*K2**2 + 56*K2*K3*K5 - 1316*K3**2 - 334*K4**2 - 8*K5**2 + 3716 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.736'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.4757', 'vk6.5086', 'vk6.6307', 'vk6.6748', 'vk6.8268', 'vk6.8719', 'vk6.9646', 'vk6.9963', 'vk6.20395', 'vk6.21740', 'vk6.27727', 'vk6.29269', 'vk6.39169', 'vk6.41393', 'vk6.45891', 'vk6.47536', 'vk6.48789', 'vk6.49002', 'vk6.49609', 'vk6.49814', 'vk6.50809', 'vk6.51026', 'vk6.51288', 'vk6.51485', 'vk6.57264', 'vk6.58485', 'vk6.61910', 'vk6.63015', 'vk6.66877', 'vk6.67751', 'vk6.69503', 'vk6.70221'] |
| 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 | O1O2O3O4U1O5U6U5U4O6U2U3 |
| R3 orbit | {'O1O2O3O4U1O5U6U5U4O6U2U3'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U2U3O5U1U6U5O6U4 |
| Gauss code of K* | O1O2O3U1O4O5U6U4U5U3O6U2 |
| Gauss code of -K* | O1O2O3U2O4U1U5U6U4O5O6U3 |
| 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 0 2 2 1 -2],[ 3 0 2 3 1 0 2],[ 0 -2 0 1 1 1 -2],[-2 -3 -1 0 1 1 -4],[-2 -1 -1 -1 0 0 -3],[-1 0 -1 -1 0 0 -1],[ 2 -2 2 4 3 1 0]] |
| Primitive based matrix | [[ 0 2 2 1 0 -2 -3],[-2 0 1 1 -1 -4 -3],[-2 -1 0 0 -1 -3 -1],[-1 -1 0 0 -1 -1 0],[ 0 1 1 1 0 -2 -2],[ 2 4 3 1 2 0 -2],[ 3 3 1 0 2 2 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-2,-1,0,2,3,-1,-1,1,4,3,0,1,3,1,1,1,0,2,2,2] |
| Phi over symmetry | [-3,-2,0,1,2,2,-1,1,4,2,4,0,2,0,1,0,1,1,2,1,-1] |
| Phi of -K | [-3,-2,0,1,2,2,-1,1,4,2,4,0,2,0,1,0,1,1,2,1,-1] |
| Phi of K* | [-2,-2,-1,0,2,3,-1,1,1,1,4,2,1,0,2,0,2,4,0,1,-1] |
| Phi of -K* | [-3,-2,0,1,2,2,2,2,0,1,3,2,1,3,4,1,1,1,0,-1,-1] |
| Symmetry type of based matrix | c |
| u-polynomial | t^3-t^2-t |
| Normalized Jones-Krushkal polynomial | 3z^2+20z+29 |
| Enhanced Jones-Krushkal polynomial | 3w^3z^2-4w^3z+24w^2z+29w |
| Inner characteristic polynomial | t^6+53t^4+28t^2+1 |
| Outer characteristic polynomial | t^7+75t^5+63t^3+9t |
| Flat arrow polynomial | 4*K1**3 - 10*K1**2 - 2*K1*K2 - 2*K1 + 5*K2 + 6 |
| 2-strand cable arrow polynomial | 256*K1**4*K2**3 - 832*K1**4*K2**2 + 1024*K1**4*K2 - 1376*K1**4 + 192*K1**3*K2*K3 + 32*K1**3*K3*K4 - 64*K1**3*K3 - 832*K1**2*K2**4 + 3328*K1**2*K2**3 - 8320*K1**2*K2**2 - 640*K1**2*K2*K4 + 7976*K1**2*K2 - 128*K1**2*K3**2 - 32*K1**2*K4**2 - 5364*K1**2 + 672*K1*K2**3*K3 - 800*K1*K2**2*K3 - 96*K1*K2**2*K5 + 5792*K1*K2*K3 + 632*K1*K3*K4 + 24*K1*K4*K5 - 32*K2**6 + 32*K2**4*K4 - 1704*K2**4 - 176*K2**2*K3**2 - 8*K2**2*K4**2 + 904*K2**2*K4 - 2576*K2**2 + 56*K2*K3*K5 - 1316*K3**2 - 334*K4**2 - 8*K5**2 + 3716 |
| 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}, {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}, {2, 4}, {3}, {1}], [{6}, {5}, {3, 4}, {1, 2}]] |
| If K is slice | False |