| Min(phi) over symmetries of the knot is: [-3,-1,1,1,1,1,0,1,2,3,3,1,1,1,2,-1,-1,-1,0,0,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.1362'] |
| Arrow polynomial of the knot is: -8*K1**2 - 2*K1*K2 + K1 + 4*K2 + K3 + 5 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.377', '6.638', '6.646', '6.647', '6.657', '6.658', '6.662', '6.692', '6.695', '6.714', '6.720', '6.726', '6.730', '6.731', '6.749', '6.756', '6.772', '6.779', '6.781', '6.800', '6.829', '6.1085', '6.1089', '6.1302', '6.1349', '6.1350', '6.1360', '6.1362', '6.1375', '6.1384'] |
| Outer characteristic polynomial of the knot is: t^7+47t^5+47t^3+5t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1362'] |
| 2-strand cable arrow polynomial of the knot is: -256*K1**6 - 128*K1**4*K2**2 + 1120*K1**4*K2 - 2752*K1**4 + 448*K1**3*K2*K3 + 32*K1**3*K3*K4 - 1280*K1**3*K3 - 1872*K1**2*K2**2 - 288*K1**2*K2*K4 + 6184*K1**2*K2 - 512*K1**2*K3**2 - 80*K1**2*K4**2 - 3888*K1**2 - 96*K1*K2**2*K3 - 32*K1*K2*K3*K4 + 3904*K1*K2*K3 + 808*K1*K3*K4 + 112*K1*K4*K5 - 32*K2**4 - 16*K2**2*K3**2 - 8*K2**2*K4**2 + 232*K2**2*K4 - 2966*K2**2 + 40*K2*K3*K5 + 8*K2*K4*K6 - 1400*K3**2 - 356*K4**2 - 48*K5**2 - 2*K6**2 + 3122 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1362'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.10941', 'vk6.10964', 'vk6.10972', 'vk6.10997', 'vk6.12107', 'vk6.12130', 'vk6.12138', 'vk6.12163', 'vk6.13794', 'vk6.13801', 'vk6.14215', 'vk6.14238', 'vk6.14662', 'vk6.14687', 'vk6.14865', 'vk6.14872', 'vk6.15818', 'vk6.15841', 'vk6.31813', 'vk6.31838', 'vk6.33624', 'vk6.33633', 'vk6.33657', 'vk6.33664', 'vk6.51785', 'vk6.51794', 'vk6.52648', 'vk6.52655', 'vk6.53804', 'vk6.53827', 'vk6.54233', 'vk6.54240'] |
| 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 | O1O2O3U2O4O5U3U6U4O6U1U5 |
| R3 orbit | {'O1O2O3U2O4O5U3U6U4O6U1U5'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U4U3O5U6U5U1O4O6U2 |
| Gauss code of K* | O1O2O3U2O4O5U4U6U1O6U3U5 |
| Gauss code of -K* | O1O2O3U4U1O5U3U5U6O4O6U2 |
| 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 3 -1],[ 1 0 -1 0 2 3 0],[ 1 1 0 1 1 1 1],[ 1 0 -1 0 1 2 0],[-1 -2 -1 -1 0 0 -1],[-3 -3 -1 -2 0 0 -3],[ 1 0 -1 0 1 3 0]] |
| Primitive based matrix | [[ 0 3 1 -1 -1 -1 -1],[-3 0 0 -1 -2 -3 -3],[-1 0 0 -1 -1 -1 -2],[ 1 1 1 0 1 1 1],[ 1 2 1 -1 0 0 0],[ 1 3 1 -1 0 0 0],[ 1 3 2 -1 0 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-3,-1,1,1,1,1,0,1,2,3,3,1,1,1,2,-1,-1,-1,0,0,0] |
| Phi over symmetry | [-3,-1,1,1,1,1,0,1,2,3,3,1,1,1,2,-1,-1,-1,0,0,0] |
| Phi of -K | [-1,-1,-1,-1,1,3,-1,-1,-1,1,3,0,0,0,1,0,1,1,1,2,2] |
| Phi of K* | [-3,-1,1,1,1,1,2,1,1,2,3,0,1,1,1,0,0,-1,0,-1,-1] |
| Phi of -K* | [-1,-1,-1,-1,1,3,-1,0,0,1,2,1,1,1,1,0,1,3,2,3,0] |
| Symmetry type of based matrix | c |
| u-polynomial | -t^3+3t |
| Normalized Jones-Krushkal polynomial | z^2+18z+33 |
| Enhanced Jones-Krushkal polynomial | w^3z^2+18w^2z+33w |
| Inner characteristic polynomial | t^6+33t^4+21t^2+1 |
| Outer characteristic polynomial | t^7+47t^5+47t^3+5t |
| Flat arrow polynomial | -8*K1**2 - 2*K1*K2 + K1 + 4*K2 + K3 + 5 |
| 2-strand cable arrow polynomial | -256*K1**6 - 128*K1**4*K2**2 + 1120*K1**4*K2 - 2752*K1**4 + 448*K1**3*K2*K3 + 32*K1**3*K3*K4 - 1280*K1**3*K3 - 1872*K1**2*K2**2 - 288*K1**2*K2*K4 + 6184*K1**2*K2 - 512*K1**2*K3**2 - 80*K1**2*K4**2 - 3888*K1**2 - 96*K1*K2**2*K3 - 32*K1*K2*K3*K4 + 3904*K1*K2*K3 + 808*K1*K3*K4 + 112*K1*K4*K5 - 32*K2**4 - 16*K2**2*K3**2 - 8*K2**2*K4**2 + 232*K2**2*K4 - 2966*K2**2 + 40*K2*K3*K5 + 8*K2*K4*K6 - 1400*K3**2 - 356*K4**2 - 48*K5**2 - 2*K6**2 + 3122 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {3, 5}, {2, 4}], [{1, 6}, {4, 5}, {2, 3}], [{3, 6}, {1, 5}, {2, 4}], [{5, 6}, {2, 4}, {1, 3}]] |
| If K is slice | False |