| Min(phi) over symmetries of the knot is: [-3,-1,0,0,1,3,1,0,2,3,4,-1,1,0,1,0,1,1,0,2,1] |
| Flat knots (up to 7 crossings) with same phi are :['6.957'] |
| Arrow polynomial of the knot is: 8*K1**3 - 4*K1**2 - 4*K1*K2 - 4*K1 + 2*K2 + 3 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.206', '6.236', '6.575', '6.580', '6.613', '6.619', '6.810', '6.819', '6.831', '6.838', '6.957', '6.1018', '6.1028', '6.1046', '6.1073', '6.1279', '6.1507', '6.1532', '6.1556', '6.1639', '6.1688', '6.1924', '6.1931'] |
| Outer characteristic polynomial of the knot is: t^7+60t^5+188t^3+27t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.957'] |
| 2-strand cable arrow polynomial of the knot is: -192*K1**4 + 448*K1**2*K2**3 - 3376*K1**2*K2**2 - 224*K1**2*K2*K4 + 4488*K1**2*K2 - 3680*K1**2 + 448*K1*K2**3*K3 - 672*K1*K2**2*K3 - 160*K1*K2**2*K5 - 96*K1*K2*K3*K4 + 4048*K1*K2*K3 + 312*K1*K3*K4 + 8*K1*K4*K5 - 1152*K2**6 + 1344*K2**4*K4 - 4368*K2**4 - 256*K2**3*K6 - 496*K2**2*K3**2 - 384*K2**2*K4**2 + 3600*K2**2*K4 - 1232*K2**2 + 312*K2*K3*K5 + 144*K2*K4*K6 - 1140*K3**2 - 620*K4**2 - 28*K5**2 - 8*K6**2 + 2930 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.957'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.72618', 'vk6.72619', 'vk6.72762', 'vk6.72763', 'vk6.73078', 'vk6.73079', 'vk6.73163', 'vk6.73164', 'vk6.73782', 'vk6.73784', 'vk6.73920', 'vk6.73922', 'vk6.75718', 'vk6.75720', 'vk6.75924', 'vk6.77871', 'vk6.77917', 'vk6.77918', 'vk6.78014', 'vk6.78727', 'vk6.78729', 'vk6.78930', 'vk6.80340', 'vk6.80342', 'vk6.81179', 'vk6.81188', 'vk6.81776', 'vk6.82476', 'vk6.87291', 'vk6.87896', 'vk6.88418', 'vk6.88424'] |
| 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 | O1O2O3O4U5U2O6O5U1U6U3U4 |
| R3 orbit | {'O1O2O3O4U5U2O6O5U1U6U3U4'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U1U2U5U4O6O5U3U6 |
| Gauss code of K* | O1O2O3O4U1U5U3U4O6O5U2U6 |
| Gauss code of -K* | O1O2O3O4U5U3O6O5U1U2U6U4 |
| 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 -1 1 3 0 0],[ 3 0 1 3 4 2 0],[ 1 -1 0 0 1 1 -1],[-1 -3 0 0 1 0 -1],[-3 -4 -1 -1 0 -2 -1],[ 0 -2 -1 0 2 0 0],[ 0 0 1 1 1 0 0]] |
| Primitive based matrix | [[ 0 3 1 0 0 -1 -3],[-3 0 -1 -1 -2 -1 -4],[-1 1 0 -1 0 0 -3],[ 0 1 1 0 0 1 0],[ 0 2 0 0 0 -1 -2],[ 1 1 0 -1 1 0 -1],[ 3 4 3 0 2 1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-3,-1,0,0,1,3,1,1,2,1,4,1,0,0,3,0,-1,0,1,2,1] |
| Phi over symmetry | [-3,-1,0,0,1,3,1,0,2,3,4,-1,1,0,1,0,1,1,0,2,1] |
| Phi of -K | [-3,-1,0,0,1,3,1,1,3,1,2,0,2,2,3,0,1,1,0,2,1] |
| Phi of K* | [-3,-1,0,0,1,3,1,1,2,3,2,1,0,2,1,0,0,1,2,3,1] |
| Phi of -K* | [-3,-1,0,0,1,3,1,0,2,3,4,-1,1,0,1,0,1,1,0,2,1] |
| Symmetry type of based matrix | c |
| u-polynomial | 0 |
| Normalized Jones-Krushkal polynomial | 5z+11 |
| Enhanced Jones-Krushkal polynomial | -6w^4z^2+6w^3z^2-16w^3z+21w^2z+11w |
| Inner characteristic polynomial | t^6+40t^4+86t^2+9 |
| Outer characteristic polynomial | t^7+60t^5+188t^3+27t |
| Flat arrow polynomial | 8*K1**3 - 4*K1**2 - 4*K1*K2 - 4*K1 + 2*K2 + 3 |
| 2-strand cable arrow polynomial | -192*K1**4 + 448*K1**2*K2**3 - 3376*K1**2*K2**2 - 224*K1**2*K2*K4 + 4488*K1**2*K2 - 3680*K1**2 + 448*K1*K2**3*K3 - 672*K1*K2**2*K3 - 160*K1*K2**2*K5 - 96*K1*K2*K3*K4 + 4048*K1*K2*K3 + 312*K1*K3*K4 + 8*K1*K4*K5 - 1152*K2**6 + 1344*K2**4*K4 - 4368*K2**4 - 256*K2**3*K6 - 496*K2**2*K3**2 - 384*K2**2*K4**2 + 3600*K2**2*K4 - 1232*K2**2 + 312*K2*K3*K5 + 144*K2*K4*K6 - 1140*K3**2 - 620*K4**2 - 28*K5**2 - 8*K6**2 + 2930 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{2, 6}, {1, 5}, {3, 4}], [{2, 6}, {1, 5}, {4}, {3}], [{5, 6}, {1, 4}, {2, 3}]] |
| If K is slice | False |