| Min(phi) over symmetries of the knot is: [-3,-1,0,1,1,2,0,0,2,3,3,0,1,1,1,0,1,0,0,0,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.1169'] |
| Arrow polynomial of the knot is: -2*K1**2 - 2*K1*K2 + K1 + K2 + K3 + 2 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.217', '6.219', '6.304', '6.349', '6.390', '6.400', '6.416', '6.515', '6.518', '6.530', '6.582', '6.616', '6.629', '6.641', '6.645', '6.702', '6.710', '6.715', '6.729', '6.733', '6.734', '6.802', '6.840', '6.845', '6.854', '6.860', '6.900', '6.905', '6.921', '6.924', '6.979', '6.980', '6.996', '6.1044', '6.1067', '6.1086', '6.1100', '6.1139', '6.1145', '6.1149', '6.1167', '6.1169', '6.1183', '6.1314'] |
| Outer characteristic polynomial of the knot is: t^7+52t^5+47t^3+5t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1169'] |
| 2-strand cable arrow polynomial of the knot is: -16*K1**4 + 32*K1**3*K2*K3 - 1952*K1**2*K2**2 - 192*K1**2*K2*K4 + 3000*K1**2*K2 - 112*K1**2*K3**2 - 3188*K1**2 + 96*K1*K2**3*K3 + 224*K1*K2**2*K3*K4 - 672*K1*K2**2*K3 - 32*K1*K2*K3*K4 + 3744*K1*K2*K3 - 224*K1*K2*K4*K5 + 1000*K1*K3*K4 + 96*K1*K4*K5 + 32*K1*K5*K6 - 72*K2**4 - 464*K2**2*K3**2 - 488*K2**2*K4**2 + 1368*K2**2*K4 - 3118*K2**2 - 96*K2*K3**2*K4 + 400*K2*K3*K5 + 472*K2*K4*K6 + 8*K3**2*K6 - 1560*K3**2 - 946*K4**2 - 124*K5**2 - 82*K6**2 + 2864 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1169'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.11077', 'vk6.11155', 'vk6.12243', 'vk6.12350', 'vk6.18328', 'vk6.18665', 'vk6.24764', 'vk6.25221', 'vk6.30660', 'vk6.30751', 'vk6.31888', 'vk6.31956', 'vk6.36950', 'vk6.37412', 'vk6.44143', 'vk6.44464', 'vk6.51866', 'vk6.51911', 'vk6.52733', 'vk6.52840', 'vk6.56106', 'vk6.56325', 'vk6.60623', 'vk6.60954', 'vk6.63526', 'vk6.63570', 'vk6.64008', 'vk6.64052', 'vk6.65754', 'vk6.66018', 'vk6.68764', 'vk6.68972'] |
| 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 | O1O2O3O4U1U5U3O5O6U4U2U6 |
| R3 orbit | {'O1O2O3O4U1U5U3O5O6U4U2U6'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U5U3U1O5O6U2U6U4 |
| Gauss code of K* | O1O2O3U2U4O5O6O4U1U6U3U5 |
| Gauss code of -K* | O1O2O3U1U4O5O4O6U3U5U2U6 |
| 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 1 1 -1 2],[ 3 0 3 1 2 2 2],[ 0 -3 0 0 1 -1 2],[-1 -1 0 0 0 -1 1],[-1 -2 -1 0 0 -1 1],[ 1 -2 1 1 1 0 2],[-2 -2 -2 -1 -1 -2 0]] |
| Primitive based matrix | [[ 0 2 1 1 0 -1 -3],[-2 0 -1 -1 -2 -2 -2],[-1 1 0 0 0 -1 -1],[-1 1 0 0 -1 -1 -2],[ 0 2 0 1 0 -1 -3],[ 1 2 1 1 1 0 -2],[ 3 2 1 2 3 2 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,-1,0,1,3,1,1,2,2,2,0,0,1,1,1,1,2,1,3,2] |
| Phi over symmetry | [-3,-1,0,1,1,2,0,0,2,3,3,0,1,1,1,0,1,0,0,0,0] |
| Phi of -K | [-3,-1,0,1,1,2,0,0,2,3,3,0,1,1,1,0,1,0,0,0,0] |
| Phi of K* | [-2,-1,-1,0,1,3,0,0,0,1,3,0,0,1,2,1,1,3,0,0,0] |
| Phi of -K* | [-3,-1,0,1,1,2,2,3,1,2,2,1,1,1,2,0,1,2,0,1,1] |
| Symmetry type of based matrix | c |
| u-polynomial | t^3-t^2-t |
| Normalized Jones-Krushkal polynomial | 6z^2+23z+23 |
| Enhanced Jones-Krushkal polynomial | 6w^3z^2+23w^2z+23w |
| Inner characteristic polynomial | t^6+36t^4+18t^2+1 |
| Outer characteristic polynomial | t^7+52t^5+47t^3+5t |
| Flat arrow polynomial | -2*K1**2 - 2*K1*K2 + K1 + K2 + K3 + 2 |
| 2-strand cable arrow polynomial | -16*K1**4 + 32*K1**3*K2*K3 - 1952*K1**2*K2**2 - 192*K1**2*K2*K4 + 3000*K1**2*K2 - 112*K1**2*K3**2 - 3188*K1**2 + 96*K1*K2**3*K3 + 224*K1*K2**2*K3*K4 - 672*K1*K2**2*K3 - 32*K1*K2*K3*K4 + 3744*K1*K2*K3 - 224*K1*K2*K4*K5 + 1000*K1*K3*K4 + 96*K1*K4*K5 + 32*K1*K5*K6 - 72*K2**4 - 464*K2**2*K3**2 - 488*K2**2*K4**2 + 1368*K2**2*K4 - 3118*K2**2 - 96*K2*K3**2*K4 + 400*K2*K3*K5 + 472*K2*K4*K6 + 8*K3**2*K6 - 1560*K3**2 - 946*K4**2 - 124*K5**2 - 82*K6**2 + 2864 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {2, 5}, {3, 4}], [{1, 6}, {4, 5}, {2, 3}], [{2, 6}, {4, 5}, {1, 3}], [{3, 6}, {4, 5}, {1, 2}]] |
| If K is slice | False |