| Min(phi) over symmetries of the knot is: [-2,-1,0,1,1,1,0,2,2,2,2,1,0,1,1,1,0,1,-1,0,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.1744'] |
| Arrow polynomial of the knot is: -14*K1**2 - 4*K1*K2 + 2*K1 + 7*K2 + 2*K3 + 8 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.665', '6.1301', '6.1514', '6.1646', '6.1669', '6.1709', '6.1710', '6.1744', '6.1776'] |
| Outer characteristic polynomial of the knot is: t^7+30t^5+41t^3+9t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1744'] |
| 2-strand cable arrow polynomial of the knot is: -576*K1**6 - 448*K1**4*K2**2 + 2176*K1**4*K2 - 5840*K1**4 + 576*K1**3*K2*K3 + 64*K1**3*K3*K4 - 576*K1**3*K3 + 1248*K1**2*K2**3 - 8784*K1**2*K2**2 - 672*K1**2*K2*K4 + 11128*K1**2*K2 - 1040*K1**2*K3**2 - 272*K1**2*K4**2 - 3920*K1**2 - 1088*K1*K2**2*K3 - 256*K1*K2*K3*K4 + 8512*K1*K2*K3 + 1800*K1*K3*K4 + 312*K1*K4*K5 - 1816*K2**4 - 320*K2**2*K3**2 - 48*K2**2*K4**2 + 1968*K2**2*K4 - 4028*K2**2 + 424*K2*K3*K5 + 32*K2*K4*K6 - 2284*K3**2 - 902*K4**2 - 164*K5**2 - 4*K6**2 + 4796 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1744'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.11261', 'vk6.11341', 'vk6.12522', 'vk6.12635', 'vk6.17608', 'vk6.18919', 'vk6.18997', 'vk6.19348', 'vk6.19643', 'vk6.24060', 'vk6.24154', 'vk6.25515', 'vk6.25616', 'vk6.26124', 'vk6.26544', 'vk6.30943', 'vk6.31068', 'vk6.32119', 'vk6.32240', 'vk6.36411', 'vk6.37660', 'vk6.37709', 'vk6.43510', 'vk6.44785', 'vk6.52027', 'vk6.52116', 'vk6.52938', 'vk6.56500', 'vk6.56648', 'vk6.65391', 'vk6.66128', 'vk6.66164'] |
| 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 | O1O2O3U4U1O4O5U6U3O6U2U5 |
| R3 orbit | {'O1O2O3U4U1O4O5U6U3O6U2U5'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U4U2O5U1U5O4O6U3U6 |
| Gauss code of K* | O1O2U1O3O4U5U3U2O6O5U6U4 |
| Gauss code of -K* | O1O2U3O4O3U1U5O6O5U4U2U6 |
| 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 0 1 -1 2 -1],[ 1 0 1 0 1 2 0],[ 0 -1 0 1 0 2 -1],[-1 0 -1 0 -1 0 -1],[ 1 -1 0 1 0 2 0],[-2 -2 -2 0 -2 0 -2],[ 1 0 1 1 0 2 0]] |
| Primitive based matrix | [[ 0 2 1 0 -1 -1 -1],[-2 0 0 -2 -2 -2 -2],[-1 0 0 -1 0 -1 -1],[ 0 2 1 0 -1 0 -1],[ 1 2 0 1 0 1 0],[ 1 2 1 0 -1 0 0],[ 1 2 1 1 0 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,0,1,1,1,0,2,2,2,2,1,0,1,1,1,0,1,-1,0,0] |
| Phi over symmetry | [-2,-1,0,1,1,1,0,2,2,2,2,1,0,1,1,1,0,1,-1,0,0] |
| Phi of -K | [-1,-1,-1,0,1,2,-1,0,0,2,1,0,1,1,1,0,1,1,0,0,1] |
| Phi of K* | [-2,-1,0,1,1,1,1,0,1,1,1,0,1,1,2,0,1,0,0,0,-1] |
| Phi of -K* | [-1,-1,-1,0,1,2,-1,0,0,1,2,0,1,0,2,1,1,2,1,2,0] |
| 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+24t^2+4 |
| Outer characteristic polynomial | t^7+30t^5+41t^3+9t |
| Flat arrow polynomial | -14*K1**2 - 4*K1*K2 + 2*K1 + 7*K2 + 2*K3 + 8 |
| 2-strand cable arrow polynomial | -576*K1**6 - 448*K1**4*K2**2 + 2176*K1**4*K2 - 5840*K1**4 + 576*K1**3*K2*K3 + 64*K1**3*K3*K4 - 576*K1**3*K3 + 1248*K1**2*K2**3 - 8784*K1**2*K2**2 - 672*K1**2*K2*K4 + 11128*K1**2*K2 - 1040*K1**2*K3**2 - 272*K1**2*K4**2 - 3920*K1**2 - 1088*K1*K2**2*K3 - 256*K1*K2*K3*K4 + 8512*K1*K2*K3 + 1800*K1*K3*K4 + 312*K1*K4*K5 - 1816*K2**4 - 320*K2**2*K3**2 - 48*K2**2*K4**2 + 1968*K2**2*K4 - 4028*K2**2 + 424*K2*K3*K5 + 32*K2*K4*K6 - 2284*K3**2 - 902*K4**2 - 164*K5**2 - 4*K6**2 + 4796 |
| 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}, {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}, {2, 4}, {3}, {1}], [{6}, {5}, {3, 4}, {1, 2}], [{6}, {5}, {3, 4}, {2}, {1}], [{6}, {5}, {4}, {1, 3}, {2}], [{6}, {5}, {4}, {2, 3}, {1}], [{6}, {5}, {4}, {3}, {1, 2}]] |
| If K is slice | False |