| Min(phi) over symmetries of the knot is: [-2,-2,1,1,1,1,-1,1,1,2,2,0,1,1,2,0,0,-1,-1,-1,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.1653'] |
| Arrow polynomial of the knot is: -8*K1**2 - 4*K1*K2 + 2*K1 + 4*K2 + 2*K3 + 5 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.235', '6.379', '6.411', '6.547', '6.811', '6.818', '6.823', '6.897', '6.898', '6.1008', '6.1053', '6.1109', '6.1110', '6.1130', '6.1222', '6.1239', '6.1303', '6.1307', '6.1342', '6.1491', '6.1495', '6.1496', '6.1519', '6.1592', '6.1593', '6.1642', '6.1652', '6.1653', '6.1671', '6.1673', '6.1717'] |
| Outer characteristic polynomial of the knot is: t^7+32t^5+39t^3+5t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1653'] |
| 2-strand cable arrow polynomial of the knot is: -448*K1**4*K2**2 + 1216*K1**4*K2 - 2032*K1**4 + 448*K1**3*K2*K3 + 32*K1**3*K3*K4 - 576*K1**3*K3 + 320*K1**2*K2**3 - 3696*K1**2*K2**2 - 416*K1**2*K2*K4 + 6000*K1**2*K2 - 368*K1**2*K3**2 - 96*K1**2*K3*K5 - 96*K1**2*K4**2 - 4088*K1**2 - 384*K1*K2**2*K3 - 32*K1*K2**2*K5 - 96*K1*K2*K3*K4 + 4408*K1*K2*K3 + 1128*K1*K3*K4 + 288*K1*K4*K5 - 192*K2**4 - 80*K2**2*K3**2 - 48*K2**2*K4**2 + 592*K2**2*K4 - 3068*K2**2 + 232*K2*K3*K5 + 32*K2*K4*K6 - 1500*K3**2 - 608*K4**2 - 164*K5**2 - 4*K6**2 + 3294 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1653'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.4433', 'vk6.4530', 'vk6.5815', 'vk6.5944', 'vk6.7880', 'vk6.7993', 'vk6.9302', 'vk6.9423', 'vk6.10161', 'vk6.10232', 'vk6.10379', 'vk6.17876', 'vk6.17941', 'vk6.18273', 'vk6.18610', 'vk6.24383', 'vk6.25161', 'vk6.30056', 'vk6.30117', 'vk6.36883', 'vk6.37343', 'vk6.43818', 'vk6.44100', 'vk6.44425', 'vk6.48624', 'vk6.50527', 'vk6.50614', 'vk6.51132', 'vk6.51676', 'vk6.55829', 'vk6.56076', 'vk6.65499'] |
| 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 | O1O2O3U1O4U5U4U2O5O6U3U6 |
| R3 orbit | {'O1O2O3U1O4U5U4U2O5O6U3U6'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U4U1O4O5U2U6U5O6U3 |
| Gauss code of K* | O1O2O3U1U4O5O4U6U3U5O6U2 |
| Gauss code of -K* | O1O2O3U2O4U5U1U4O6O5U6U3 |
| 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 1 -2 1],[ 2 0 1 2 0 1 1],[-1 -1 0 0 0 -2 1],[-1 -2 0 0 1 -2 1],[-1 0 0 -1 0 -1 0],[ 2 -1 2 2 1 0 1],[-1 -1 -1 -1 0 -1 0]] |
| Primitive based matrix | [[ 0 1 1 1 1 -2 -2],[-1 0 1 1 0 -2 -2],[-1 -1 0 0 0 0 -1],[-1 -1 0 0 -1 -1 -1],[-1 0 0 1 0 -1 -2],[ 2 2 0 1 1 0 1],[ 2 2 1 1 2 -1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-1,-1,-1,-1,2,2,-1,-1,0,2,2,0,0,0,1,1,1,1,1,2,-1] |
| Phi over symmetry | [-2,-2,1,1,1,1,-1,1,1,2,2,0,1,1,2,0,0,-1,-1,-1,0] |
| Phi of -K | [-2,-2,1,1,1,1,-1,1,2,2,3,1,1,2,2,0,-1,-1,-1,0,0] |
| Phi of K* | [-1,-1,-1,-1,2,2,-1,-1,0,2,2,0,0,1,2,1,1,1,2,3,-1] |
| Phi of -K* | [-2,-2,1,1,1,1,-1,1,1,2,2,0,1,1,2,0,0,-1,-1,-1,0] |
| Symmetry type of based matrix | c |
| u-polynomial | 2t^2-4t |
| Normalized Jones-Krushkal polynomial | 2z^2+19z+31 |
| Enhanced Jones-Krushkal polynomial | 2w^3z^2+19w^2z+31w |
| Inner characteristic polynomial | t^6+20t^4+21t^2+1 |
| Outer characteristic polynomial | t^7+32t^5+39t^3+5t |
| Flat arrow polynomial | -8*K1**2 - 4*K1*K2 + 2*K1 + 4*K2 + 2*K3 + 5 |
| 2-strand cable arrow polynomial | -448*K1**4*K2**2 + 1216*K1**4*K2 - 2032*K1**4 + 448*K1**3*K2*K3 + 32*K1**3*K3*K4 - 576*K1**3*K3 + 320*K1**2*K2**3 - 3696*K1**2*K2**2 - 416*K1**2*K2*K4 + 6000*K1**2*K2 - 368*K1**2*K3**2 - 96*K1**2*K3*K5 - 96*K1**2*K4**2 - 4088*K1**2 - 384*K1*K2**2*K3 - 32*K1*K2**2*K5 - 96*K1*K2*K3*K4 + 4408*K1*K2*K3 + 1128*K1*K3*K4 + 288*K1*K4*K5 - 192*K2**4 - 80*K2**2*K3**2 - 48*K2**2*K4**2 + 592*K2**2*K4 - 3068*K2**2 + 232*K2*K3*K5 + 32*K2*K4*K6 - 1500*K3**2 - 608*K4**2 - 164*K5**2 - 4*K6**2 + 3294 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{2, 6}, {3, 5}, {1, 4}], [{2, 6}, {4, 5}, {1, 3}], [{3, 6}, {2, 5}, {1, 4}], [{3, 6}, {4, 5}, {1, 2}], [{4, 6}, {2, 5}, {1, 3}], [{4, 6}, {3, 5}, {1, 2}]] |
| If K is slice | False |