| Min(phi) over symmetries of the knot is: [-1,-1,-1,1,1,1,-1,-1,1,1,1,-1,1,1,1,0,1,1,-1,0,1] |
| Flat knots (up to 7 crossings) with same phi are :['6.414', '6.1611', '7.14293', '7.20044', '7.25964'] |
| Arrow polynomial of the knot is: 8*K1**3 - 8*K1**2 - 8*K1*K2 - 2*K1 + 4*K2 + 2*K3 + 5 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.414', '6.594', '6.608', '6.790', '6.1233', '6.1285', '6.1293', '6.1513', '6.1752', '6.1787', '6.1810', '6.1818', '6.1867', '6.1868', '6.1923'] |
| Outer characteristic polynomial of the knot is: t^7+19t^5+23t^3+5t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.414', '6.1611', '7.20044'] |
| 2-strand cable arrow polynomial of the knot is: -2048*K1**6 - 4352*K1**4*K2**2 + 7424*K1**4*K2 - 7584*K1**4 + 3520*K1**3*K2*K3 - 1184*K1**3*K3 - 3136*K1**2*K2**4 + 7552*K1**2*K2**3 + 1024*K1**2*K2**2*K4 - 16256*K1**2*K2**2 - 1792*K1**2*K2*K4 + 9648*K1**2*K2 - 896*K1**2*K3**2 - 224*K1**2*K4**2 + 1640*K1**2 + 3648*K1*K2**3*K3 - 2848*K1*K2**2*K3 - 864*K1*K2**2*K5 - 448*K1*K2*K3*K4 + 7424*K1*K2*K3 + 592*K1*K3*K4 + 144*K1*K4*K5 - 704*K2**6 + 1088*K2**4*K4 - 4384*K2**4 - 192*K2**3*K6 - 896*K2**2*K3**2 - 384*K2**2*K4**2 + 2480*K2**2*K4 + 772*K2**2 + 336*K2*K3*K5 + 112*K2*K4*K6 - 404*K3**2 - 120*K4**2 - 20*K5**2 - 4*K6**2 + 1334 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.414'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.75', 'vk6.79', 'vk6.134', 'vk6.142', 'vk6.229', 'vk6.237', 'vk6.274', 'vk6.278', 'vk6.394', 'vk6.395', 'vk6.818', 'vk6.819', 'vk6.1278', 'vk6.1286', 'vk6.1367', 'vk6.1375', 'vk6.1414', 'vk6.1418', 'vk6.1559', 'vk6.1560', 'vk6.2687', 'vk6.2688', 'vk6.2941', 'vk6.2949', 'vk6.14842', 'vk6.14850', 'vk6.15998', 'vk6.16006', 'vk6.25967', 'vk6.25968', 'vk6.33344', 'vk6.33363'] |
| 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 | O1O2O3O4O5U4U5O6U3U6U1U2 |
| R3 orbit | {'O1O2O3O4O5U4U5O6U3U6U1U2'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4O5U4U5U6U3O6U1U2 |
| Gauss code of K* | O1O2O3O4U3U4U1U5U6O5O6U2 |
| Gauss code of -K* | O1O2O3O4U3O5O6U5U6U4U1U2 |
| 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 -1 1 -1 -1 1 1],[ 1 0 1 -1 -1 1 1],[-1 -1 0 -1 -1 1 1],[ 1 1 1 0 -1 1 1],[ 1 1 1 1 0 1 0],[-1 -1 -1 -1 -1 0 0],[-1 -1 -1 -1 0 0 0]] |
| Primitive based matrix | [[ 0 1 1 1 -1 -1 -1],[-1 0 1 1 -1 -1 -1],[-1 -1 0 0 0 -1 -1],[-1 -1 0 0 -1 -1 -1],[ 1 1 0 1 0 1 1],[ 1 1 1 1 -1 0 1],[ 1 1 1 1 -1 -1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-1,-1,-1,1,1,1,-1,-1,1,1,1,0,0,1,1,1,1,1,-1,-1,-1] |
| Phi over symmetry | [-1,-1,-1,1,1,1,-1,-1,1,1,1,-1,1,1,1,0,1,1,-1,0,1] |
| Phi of -K | [-1,-1,-1,1,1,1,-1,-1,1,1,2,-1,1,1,1,1,1,1,-1,-1,0] |
| Phi of K* | [-1,-1,-1,1,1,1,-1,0,1,1,1,1,1,1,1,1,1,2,-1,-1,-1] |
| Phi of -K* | [-1,-1,-1,1,1,1,-1,-1,1,1,1,-1,1,1,1,0,1,1,-1,0,1] |
| Symmetry type of based matrix | c |
| u-polynomial | 0 |
| Normalized Jones-Krushkal polynomial | 4z^2+21z+27 |
| Enhanced Jones-Krushkal polynomial | 4w^3z^2+21w^2z+27w |
| Inner characteristic polynomial | t^6+13t^4+9t^2+1 |
| Outer characteristic polynomial | t^7+19t^5+23t^3+5t |
| Flat arrow polynomial | 8*K1**3 - 8*K1**2 - 8*K1*K2 - 2*K1 + 4*K2 + 2*K3 + 5 |
| 2-strand cable arrow polynomial | -2048*K1**6 - 4352*K1**4*K2**2 + 7424*K1**4*K2 - 7584*K1**4 + 3520*K1**3*K2*K3 - 1184*K1**3*K3 - 3136*K1**2*K2**4 + 7552*K1**2*K2**3 + 1024*K1**2*K2**2*K4 - 16256*K1**2*K2**2 - 1792*K1**2*K2*K4 + 9648*K1**2*K2 - 896*K1**2*K3**2 - 224*K1**2*K4**2 + 1640*K1**2 + 3648*K1*K2**3*K3 - 2848*K1*K2**2*K3 - 864*K1*K2**2*K5 - 448*K1*K2*K3*K4 + 7424*K1*K2*K3 + 592*K1*K3*K4 + 144*K1*K4*K5 - 704*K2**6 + 1088*K2**4*K4 - 4384*K2**4 - 192*K2**3*K6 - 896*K2**2*K3**2 - 384*K2**2*K4**2 + 2480*K2**2*K4 + 772*K2**2 + 336*K2*K3*K5 + 112*K2*K4*K6 - 404*K3**2 - 120*K4**2 - 20*K5**2 - 4*K6**2 + 1334 |
| Genus of based matrix | 0 |
| Fillings of based matrix | [[{3, 6}, {4, 5}, {1, 2}]] |
| If K is slice | True |