| Min(phi) over symmetries of the knot is: [-3,-2,0,1,2,2,-1,2,1,3,3,2,1,1,2,0,1,1,-1,0,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.845'] |
| 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+69t^5+70t^3+4t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.845'] |
| 2-strand cable arrow polynomial of the knot is: -256*K1**3*K3 - 384*K1**2*K2**2 + 96*K1**2*K2*K3**2 + 2536*K1**2*K2 - 320*K1**2*K3**2 - 3056*K1**2 - 864*K1*K2**2*K3 - 96*K1*K2**2*K5 - 448*K1*K2*K3*K4 + 3008*K1*K2*K3 + 920*K1*K3*K4 + 304*K1*K4*K5 - 440*K2**4 - 480*K2**2*K3**2 - 72*K2**2*K4**2 + 1144*K2**2*K4 - 2454*K2**2 + 712*K2*K3*K5 + 72*K2*K4*K6 - 1408*K3**2 - 666*K4**2 - 264*K5**2 - 18*K6**2 + 2432 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.845'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.71579', 'vk6.71698', 'vk6.72118', 'vk6.72318', 'vk6.73486', 'vk6.74110', 'vk6.74131', 'vk6.74681', 'vk6.74701', 'vk6.75245', 'vk6.75496', 'vk6.76148', 'vk6.76174', 'vk6.77197', 'vk6.77300', 'vk6.77505', 'vk6.77657', 'vk6.78449', 'vk6.79112', 'vk6.79134', 'vk6.80037', 'vk6.80187', 'vk6.80620', 'vk6.80635', 'vk6.83736', 'vk6.83865', 'vk6.85063', 'vk6.85349', 'vk6.86672', 'vk6.86965', 'vk6.87421', 'vk6.89535'] |
| 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 | O1O2O3O4U1U3O5O6U2U4U6U5 |
| R3 orbit | {'O1O2O3O4U1U3O5O6U2U4U6U5'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U5U6U1U3O6O5U2U4 |
| Gauss code of K* | O1O2O3O4U5U1U6U2O5O6U4U3 |
| Gauss code of -K* | O1O2O3O4U2U1O5O6U3U5U4U6 |
| 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 -2 0 1 2 2],[ 3 0 2 1 3 2 2],[ 2 -2 0 0 2 3 2],[ 0 -1 0 0 1 1 1],[-1 -3 -2 -1 0 2 1],[-2 -2 -3 -1 -2 0 0],[-2 -2 -2 -1 -1 0 0]] |
| Primitive based matrix | [[ 0 2 2 1 0 -2 -3],[-2 0 0 -1 -1 -2 -2],[-2 0 0 -2 -1 -3 -2],[-1 1 2 0 -1 -2 -3],[ 0 1 1 1 0 0 -1],[ 2 2 3 2 0 0 -2],[ 3 2 2 3 1 2 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-2,-1,0,2,3,0,1,1,2,2,2,1,3,2,1,2,3,0,1,2] |
| Phi over symmetry | [-3,-2,0,1,2,2,-1,2,1,3,3,2,1,1,2,0,1,1,-1,0,0] |
| Phi of -K | [-3,-2,0,1,2,2,-1,2,1,3,3,2,1,1,2,0,1,1,-1,0,0] |
| Phi of K* | [-2,-2,-1,0,2,3,0,-1,1,1,3,0,1,2,3,0,1,1,2,2,-1] |
| Phi of -K* | [-3,-2,0,1,2,2,2,1,3,2,2,0,2,2,3,1,1,1,1,2,0] |
| 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+47t^4+15t^2 |
| Outer characteristic polynomial | t^7+69t^5+70t^3+4t |
| Flat arrow polynomial | -2*K1**2 - 2*K1*K2 + K1 + K2 + K3 + 2 |
| 2-strand cable arrow polynomial | -256*K1**3*K3 - 384*K1**2*K2**2 + 96*K1**2*K2*K3**2 + 2536*K1**2*K2 - 320*K1**2*K3**2 - 3056*K1**2 - 864*K1*K2**2*K3 - 96*K1*K2**2*K5 - 448*K1*K2*K3*K4 + 3008*K1*K2*K3 + 920*K1*K3*K4 + 304*K1*K4*K5 - 440*K2**4 - 480*K2**2*K3**2 - 72*K2**2*K4**2 + 1144*K2**2*K4 - 2454*K2**2 + 712*K2*K3*K5 + 72*K2*K4*K6 - 1408*K3**2 - 666*K4**2 - 264*K5**2 - 18*K6**2 + 2432 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{3, 6}, {1, 5}, {2, 4}], [{4, 6}, {3, 5}, {1, 2}], [{5, 6}, {1, 4}, {2, 3}]] |
| If K is slice | False |