| Min(phi) over symmetries of the knot is: [-4,0,0,1,3,1,2,4,3,0,1,1,1,2,2] |
| Flat knots (up to 7 crossings) with same phi are :['5.8'] |
| Arrow polynomial of the knot is: 2*K1**2 + 2*K1*K2 + 2*K1*K3 - K1 - 2*K2 - K3 - K4 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['5.8', '7.679', '7.806', '7.809', '7.836', '7.842', '7.1384', '7.1621', '7.2272', '7.2365', '7.2552', '7.2581', '7.2593', '7.2596', '7.2597', '7.2945', '7.2947', '7.2966', '7.2967', '7.2995', '7.3182', '7.3314', '7.3317', '7.3467', '7.3527', '7.3793', '7.4198', '7.4200', '7.4409', '7.5197', '7.5488', '7.5565', '7.5745', '7.5863', '7.5880', '7.6237', '7.6288', '7.6296', '7.6310', '7.6329', '7.6398', '7.6424', '7.6480', '7.6489', '7.6553', '7.6904', '7.7040', '7.7112', '7.7124', '7.7160', '7.7222', '7.8045', '7.8058', '7.8059', '7.8088', '7.8166', '7.8292', '7.8986', '7.8988', '7.9284', '7.9342', '7.9398', '7.9408', '7.9419', '7.9527', '7.9733', '7.9830', '7.9928', '7.9933', '7.9934', '7.10091', '7.10100', '7.10487', '7.11381', '7.11435', '7.11621', '7.11982', '7.13113', '7.13164', '7.13220', '7.13291', '7.14085', '7.14214', '7.14951', '7.14990', '7.15111', '7.15704', '7.15804', '7.16002', '7.16270', '7.16300', '7.16845', '7.16891', '7.17068'] |
| Outer characteristic polynomial of the knot is: t^6+67t^4+28t^2+1 |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['5.8'] |
| 2-strand cable arrow polynomial of the knot is: -64*K1**4 + 32*K1**3*K2*K3 - 160*K1**3*K3 - 112*K1**2*K2**2 + 128*K1**2*K2*K3**2 + 960*K1**2*K2 - 256*K1**2*K3**2 - 1232*K1**2 - 256*K1*K2**2*K3 - 96*K1*K2*K3*K4 + 1208*K1*K2*K3 + 448*K1*K3*K4 + 56*K1*K4*K5 + 8*K1*K5*K6 - 8*K2**4 - 208*K2**2*K3**2 - 8*K2**2*K4**2 + 208*K2**2*K4 - 8*K2**2*K6**2 - 954*K2**2 + 232*K2*K3*K5 + 24*K2*K4*K6 + 8*K2*K5*K7 + 8*K2*K6*K8 + 16*K3**2*K6 - 620*K3**2 + 8*K3*K4*K7 - 248*K4**2 - 92*K5**2 - 22*K6**2 - 8*K7**2 - 2*K8**2 + 1008 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['5.8'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk5.603', 'vk5.615', 'vk5.734', 'vk5.749', 'vk5.1082', 'vk5.1106', 'vk5.1252', 'vk5.1268', 'vk5.1604', 'vk5.1622', 'vk5.1717', 'vk5.1737', 'vk5.1833', 'vk5.1851', 'vk5.1903', 'vk5.1915'] |
| 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 | O1O2O3O4O5U1U4U3U5U2 |
| R3 orbit | {'O1O2O3O4O5U1U4U3U5U2'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4O5U4U1U3U2U5 |
| Gauss code of K* | O1O2O3O4O5U1U5U3U2U4 |
| Gauss code of -K* | O1O2O3O4O5U2U4U3U1U5 |
| 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 -4 1 0 0 3],[ 4 0 4 2 1 3],[-1 -4 0 -1 -1 2],[ 0 -2 1 0 0 2],[ 0 -1 1 0 0 1],[-3 -3 -2 -2 -1 0]] |
| Primitive based matrix | [[ 0 3 1 0 0 -4],[-3 0 -2 -1 -2 -3],[-1 2 0 -1 -1 -4],[ 0 1 1 0 0 -1],[ 0 2 1 0 0 -2],[ 4 3 4 1 2 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-3,-1,0,0,4,2,1,2,3,1,1,4,0,1,2] |
| Phi over symmetry | [-4,0,0,1,3,1,2,4,3,0,1,1,1,2,2] |
| Phi of -K | [-4,0,0,1,3,2,3,1,4,0,0,1,0,2,0] |
| Phi of K* | [-3,-1,0,0,4,0,1,2,4,0,0,1,0,2,3] |
| Phi of -K* | [-4,0,0,1,3,1,2,4,3,0,1,1,1,2,2] |
| Symmetry type of based matrix | c |
| u-polynomial | t^4-t^3-t |
| Normalized Jones-Krushkal polynomial | -2z^2-13z-17 |
| Enhanced Jones-Krushkal polynomial | -2w^3z^2-13w^2z-17w |
| Inner characteristic polynomial | t^5+41t^3+4t |
| Outer characteristic polynomial | t^6+67t^4+28t^2+1 |
| Flat arrow polynomial | 2*K1**2 + 2*K1*K2 + 2*K1*K3 - K1 - 2*K2 - K3 - K4 |
| 2-strand cable arrow polynomial | -64*K1**4 + 32*K1**3*K2*K3 - 160*K1**3*K3 - 112*K1**2*K2**2 + 128*K1**2*K2*K3**2 + 960*K1**2*K2 - 256*K1**2*K3**2 - 1232*K1**2 - 256*K1*K2**2*K3 - 96*K1*K2*K3*K4 + 1208*K1*K2*K3 + 448*K1*K3*K4 + 56*K1*K4*K5 + 8*K1*K5*K6 - 8*K2**4 - 208*K2**2*K3**2 - 8*K2**2*K4**2 + 208*K2**2*K4 - 8*K2**2*K6**2 - 954*K2**2 + 232*K2*K3*K5 + 24*K2*K4*K6 + 8*K2*K5*K7 + 8*K2*K6*K8 + 16*K3**2*K6 - 620*K3**2 + 8*K3*K4*K7 - 248*K4**2 - 92*K5**2 - 22*K6**2 - 8*K7**2 - 2*K8**2 + 1008 |
| Genus of based matrix | 2 |
| Fillings of based matrix | [[{1, 5}, {2, 4}, {3}], [{1, 5}, {3, 4}, {2}], [{1, 5}, {4}, {2, 3}], [{1, 5}, {4}, {3}, {2}], [{2, 5}, {1, 4}, {3}], [{2, 5}, {3, 4}, {1}], [{2, 5}, {4}, {1, 3}], [{2, 5}, {4}, {3}, {1}], [{3, 5}, {1, 4}, {2}], [{3, 5}, {2, 4}, {1}], [{3, 5}, {4}, {1, 2}], [{3, 5}, {4}, {2}, {1}], [{4, 5}, {1, 3}, {2}], [{4, 5}, {2, 3}, {1}], [{4, 5}, {3}, {1, 2}], [{4, 5}, {3}, {2}, {1}], [{5}, {1, 4}, {2, 3}], [{5}, {1, 4}, {3}, {2}], [{5}, {2, 4}, {1, 3}], [{5}, {2, 4}, {3}, {1}], [{5}, {3, 4}, {1, 2}], [{5}, {3, 4}, {2}, {1}], [{5}, {4}, {1, 3}, {2}], [{5}, {4}, {2, 3}, {1}], [{5}, {4}, {3}, {1, 2}]] |
| If K is slice | False |