| Min(phi) over symmetries of the knot is: [-3,-1,0,1,1,2,1,1,1,3,2,0,2,2,2,0,0,0,0,1,1] |
| Flat knots (up to 7 crossings) with same phi are :['6.1026'] |
| Arrow polynomial of the knot is: -6*K1**2 - 6*K1*K2 + 3*K1 + 3*K2 + 3*K3 + 4 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.458', '6.601', '6.611', '6.995', '6.1026', '6.1037'] |
| Outer characteristic polynomial of the knot is: t^7+48t^5+102t^3+10t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1026'] |
| 2-strand cable arrow polynomial of the knot is: 448*K1**4*K2 - 3120*K1**4 + 384*K1**3*K2*K3 + 32*K1**3*K3*K4 - 1152*K1**3*K3 - 2656*K1**2*K2**2 - 704*K1**2*K2*K4 + 7032*K1**2*K2 - 1440*K1**2*K3**2 - 96*K1**2*K3*K5 - 64*K1**2*K4**2 - 4876*K1**2 + 96*K1*K2**3*K3 - 544*K1*K2**2*K3 - 32*K1*K2**2*K5 - 128*K1*K2*K3*K4 + 6896*K1*K2*K3 + 2552*K1*K3*K4 + 232*K1*K4*K5 - 120*K2**4 - 336*K2**2*K3**2 - 24*K2**2*K4**2 + 768*K2**2*K4 - 4038*K2**2 + 360*K2*K3*K5 + 40*K2*K4*K6 - 48*K3**4 + 32*K3**2*K6 - 2720*K3**2 - 1034*K4**2 - 148*K5**2 - 18*K6**2 + 4424 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1026'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.11023', 'vk6.11101', 'vk6.12193', 'vk6.12300', 'vk6.18195', 'vk6.18531', 'vk6.24650', 'vk6.25077', 'vk6.30592', 'vk6.30687', 'vk6.31862', 'vk6.31908', 'vk6.36789', 'vk6.37240', 'vk6.44029', 'vk6.44370', 'vk6.51822', 'vk6.51889', 'vk6.52694', 'vk6.52788', 'vk6.55990', 'vk6.56263', 'vk6.60521', 'vk6.60863', 'vk6.63502', 'vk6.63546', 'vk6.63984', 'vk6.64028', 'vk6.65655', 'vk6.65935', 'vk6.68699', 'vk6.68909'] |
| 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 | O1O2O3O4U3U5O6U1O5U2U6U4 |
| R3 orbit | {'O1O2O3O4U3U5O6U1O5U2U6U4'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U1U5U3O6U4O5U6U2 |
| Gauss code of K* | O1O2O3U4U1U5U3O5O6U2O4U6 |
| Gauss code of -K* | O1O2O3U4O5U2O4O6U1U6U3U5 |
| 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 -2 -1 -1 3 0 1],[ 2 0 0 0 3 2 1],[ 1 0 0 0 3 1 0],[ 1 0 0 0 1 1 0],[-3 -3 -3 -1 0 -2 -1],[ 0 -2 -1 -1 2 0 1],[-1 -1 0 0 1 -1 0]] |
| Primitive based matrix | [[ 0 3 1 0 -1 -1 -2],[-3 0 -1 -2 -1 -3 -3],[-1 1 0 -1 0 0 -1],[ 0 2 1 0 -1 -1 -2],[ 1 1 0 1 0 0 0],[ 1 3 0 1 0 0 0],[ 2 3 1 2 0 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-3,-1,0,1,1,2,1,2,1,3,3,1,0,0,1,1,1,2,0,0,0] |
| Phi over symmetry | [-3,-1,0,1,1,2,1,1,1,3,2,0,2,2,2,0,0,0,0,1,1] |
| Phi of -K | [-2,-1,-1,0,1,3,1,1,0,2,2,0,0,2,1,0,2,3,0,1,1] |
| Phi of K* | [-3,-1,0,1,1,2,1,1,1,3,2,0,2,2,2,0,0,0,0,1,1] |
| Phi of -K* | [-2,-1,-1,0,1,3,0,0,2,1,3,0,1,0,1,1,0,3,1,2,1] |
| Symmetry type of based matrix | c |
| u-polynomial | -t^3+t^2+t |
| Normalized Jones-Krushkal polynomial | 5z^2+26z+33 |
| Enhanced Jones-Krushkal polynomial | 5w^3z^2+26w^2z+33w |
| Inner characteristic polynomial | t^6+32t^4+55t^2+4 |
| Outer characteristic polynomial | t^7+48t^5+102t^3+10t |
| Flat arrow polynomial | -6*K1**2 - 6*K1*K2 + 3*K1 + 3*K2 + 3*K3 + 4 |
| 2-strand cable arrow polynomial | 448*K1**4*K2 - 3120*K1**4 + 384*K1**3*K2*K3 + 32*K1**3*K3*K4 - 1152*K1**3*K3 - 2656*K1**2*K2**2 - 704*K1**2*K2*K4 + 7032*K1**2*K2 - 1440*K1**2*K3**2 - 96*K1**2*K3*K5 - 64*K1**2*K4**2 - 4876*K1**2 + 96*K1*K2**3*K3 - 544*K1*K2**2*K3 - 32*K1*K2**2*K5 - 128*K1*K2*K3*K4 + 6896*K1*K2*K3 + 2552*K1*K3*K4 + 232*K1*K4*K5 - 120*K2**4 - 336*K2**2*K3**2 - 24*K2**2*K4**2 + 768*K2**2*K4 - 4038*K2**2 + 360*K2*K3*K5 + 40*K2*K4*K6 - 48*K3**4 + 32*K3**2*K6 - 2720*K3**2 - 1034*K4**2 - 148*K5**2 - 18*K6**2 + 4424 |
| 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}], [{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}], [{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}, {3, 4}, {1, 2}]] |
| If K is slice | False |