| Min(phi) over symmetries of the knot is: [-2,-1,0,1,1,1,-1,2,1,1,1,0,0,0,1,0,1,0,0,0,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.1726', '7.44777'] |
| Arrow polynomial of the knot is: 4*K1**3 - 10*K1**2 - 4*K1*K2 - K1 + 5*K2 + K3 + 6 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.241', '6.341', '6.542', '6.567', '6.699', '6.713', '6.771', '6.791', '6.1025', '6.1039', '6.1041', '6.1072', '6.1077', '6.1121', '6.1123', '6.1499', '6.1502', '6.1531', '6.1645', '6.1648', '6.1726', '6.1727', '6.1761', '6.1784', '6.1807', '6.1823', '6.1832', '6.1869', '6.1873', '6.1874'] |
| Outer characteristic polynomial of the knot is: t^7+18t^5+31t^3+6t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1726'] |
| 2-strand cable arrow polynomial of the knot is: -1024*K1**6 - 2176*K1**4*K2**2 + 3712*K1**4*K2 - 4736*K1**4 + 1856*K1**3*K2*K3 - 448*K1**3*K3 - 1216*K1**2*K2**4 + 3904*K1**2*K2**3 + 128*K1**2*K2**2*K4 - 11200*K1**2*K2**2 - 896*K1**2*K2*K4 + 8832*K1**2*K2 - 768*K1**2*K3**2 - 96*K1**2*K3*K5 - 1436*K1**2 + 2144*K1*K2**3*K3 + 96*K1*K2**2*K3*K4 - 2560*K1*K2**2*K3 - 512*K1*K2**2*K5 - 160*K1*K2*K3*K4 - 96*K1*K2*K3*K6 + 7400*K1*K2*K3 + 984*K1*K3*K4 + 80*K1*K4*K5 - 32*K2**6 + 96*K2**4*K4 - 2824*K2**4 - 32*K2**3*K6 - 1168*K2**2*K3**2 - 112*K2**2*K4**2 + 2192*K2**2*K4 - 1638*K2**2 + 688*K2*K3*K5 + 88*K2*K4*K6 + 24*K3**2*K6 - 1260*K3**2 - 382*K4**2 - 96*K5**2 - 18*K6**2 + 2660 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1726'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.398', 'vk6.429', 'vk6.435', 'vk6.834', 'vk6.844', 'vk6.875', 'vk6.885', 'vk6.1587', 'vk6.2031', 'vk6.2038', 'vk6.2060', 'vk6.2069', 'vk6.2701', 'vk6.2735', 'vk6.2738', 'vk6.3144', 'vk6.13527', 'vk6.13547', 'vk6.13718', 'vk6.13738', 'vk6.19460', 'vk6.19465', 'vk6.19754', 'vk6.19760', 'vk6.25797', 'vk6.25805', 'vk6.26629', 'vk6.37910', 'vk6.37917', 'vk6.44913', 'vk6.53671', 'vk6.66243'] |
| 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 | O1O2O3U2U3O4O5U1U5O6U4U6 |
| R3 orbit | {'O1O2O3U2U3O4O5U1U5O6U4U6'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U4U5O4U6U3O6O5U1U2 |
| Gauss code of K* | O1O2U3O4O3U1U5U6O5O6U4U2 |
| Gauss code of -K* | O1O2U1O3O4U3U2O5O6U5U6U4 |
| 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 0 1 1],[ 2 0 -1 1 2 1 1],[ 1 1 0 1 0 0 0],[-1 -1 -1 0 0 0 0],[ 0 -2 0 0 0 0 1],[-1 -1 0 0 0 0 0],[-1 -1 0 0 -1 0 0]] |
| Primitive based matrix | [[ 0 1 1 1 0 -1 -2],[-1 0 0 0 0 0 -1],[-1 0 0 0 0 -1 -1],[-1 0 0 0 -1 0 -1],[ 0 0 0 1 0 0 -2],[ 1 0 1 0 0 0 1],[ 2 1 1 1 2 -1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-1,-1,-1,0,1,2,0,0,0,0,1,0,0,1,1,1,0,1,0,2,-1] |
| Phi over symmetry | [-2,-1,0,1,1,1,-1,2,1,1,1,0,0,0,1,0,1,0,0,0,0] |
| Phi of -K | [-2,-1,0,1,1,1,2,0,2,2,2,1,1,2,2,1,0,1,0,0,0] |
| Phi of K* | [-1,-1,-1,0,1,2,0,0,0,2,2,0,1,1,2,1,2,2,1,0,2] |
| Phi of -K* | [-2,-1,0,1,1,1,-1,2,1,1,1,0,0,0,1,0,1,0,0,0,0] |
| Symmetry type of based matrix | c |
| u-polynomial | t^2-2t |
| Normalized Jones-Krushkal polynomial | 5z^2+26z+33 |
| Enhanced Jones-Krushkal polynomial | 5w^3z^2+26w^2z+33w |
| Inner characteristic polynomial | t^6+10t^4+10t^2+1 |
| Outer characteristic polynomial | t^7+18t^5+31t^3+6t |
| Flat arrow polynomial | 4*K1**3 - 10*K1**2 - 4*K1*K2 - K1 + 5*K2 + K3 + 6 |
| 2-strand cable arrow polynomial | -1024*K1**6 - 2176*K1**4*K2**2 + 3712*K1**4*K2 - 4736*K1**4 + 1856*K1**3*K2*K3 - 448*K1**3*K3 - 1216*K1**2*K2**4 + 3904*K1**2*K2**3 + 128*K1**2*K2**2*K4 - 11200*K1**2*K2**2 - 896*K1**2*K2*K4 + 8832*K1**2*K2 - 768*K1**2*K3**2 - 96*K1**2*K3*K5 - 1436*K1**2 + 2144*K1*K2**3*K3 + 96*K1*K2**2*K3*K4 - 2560*K1*K2**2*K3 - 512*K1*K2**2*K5 - 160*K1*K2*K3*K4 - 96*K1*K2*K3*K6 + 7400*K1*K2*K3 + 984*K1*K3*K4 + 80*K1*K4*K5 - 32*K2**6 + 96*K2**4*K4 - 2824*K2**4 - 32*K2**3*K6 - 1168*K2**2*K3**2 - 112*K2**2*K4**2 + 2192*K2**2*K4 - 1638*K2**2 + 688*K2*K3*K5 + 88*K2*K4*K6 + 24*K3**2*K6 - 1260*K3**2 - 382*K4**2 - 96*K5**2 - 18*K6**2 + 2660 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {4, 5}, {2, 3}], [{2, 6}, {1, 5}, {3, 4}], [{2, 6}, {3, 5}, {1, 4}], [{2, 6}, {4, 5}, {1, 3}], [{3, 6}, {4, 5}, {1, 2}], [{4, 6}, {1, 5}, {2, 3}], [{5, 6}, {1, 4}, {2, 3}], [{6}, {4, 5}, {2, 3}, {1}]] |
| If K is slice | False |