| Min(phi) over symmetries of the knot is: [-2,-1,-1,1,1,2,-1,1,1,3,2,1,0,1,1,1,2,1,-1,0,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.1303'] |
| 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+42t^5+124t^3 |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1303'] |
| 2-strand cable arrow polynomial of the knot is: -192*K1**6 - 192*K1**4*K2**2 + 544*K1**4*K2 - 1680*K1**4 + 384*K1**3*K2*K3 + 64*K1**3*K3*K4 - 1472*K1**2*K2**2 + 2272*K1**2*K2 - 528*K1**2*K3**2 - 112*K1**2*K4**2 - 692*K1**2 + 1728*K1*K2*K3 + 440*K1*K3*K4 + 80*K1*K4*K5 - 192*K2**4 - 96*K2**2*K3**2 - 16*K2**2*K4**2 + 184*K2**2*K4 - 1028*K2**2 + 112*K2*K3*K5 + 32*K2*K4*K6 - 608*K3**2 - 184*K4**2 - 52*K5**2 - 12*K6**2 + 1214 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1303'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.11245', 'vk6.11325', 'vk6.12506', 'vk6.12619', 'vk6.13879', 'vk6.13976', 'vk6.14132', 'vk6.14357', 'vk6.14954', 'vk6.15077', 'vk6.15588', 'vk6.16060', 'vk6.17411', 'vk6.22590', 'vk6.22623', 'vk6.23923', 'vk6.24062', 'vk6.24156', 'vk6.26140', 'vk6.26559', 'vk6.30927', 'vk6.31052', 'vk6.33698', 'vk6.33775', 'vk6.34580', 'vk6.36223', 'vk6.37658', 'vk6.37707', 'vk6.42276', 'vk6.44801', 'vk6.52011', 'vk6.52104', 'vk6.54105', 'vk6.54414', 'vk6.54576', 'vk6.56498', 'vk6.56664', 'vk6.59050', 'vk6.60065', 'vk6.64569'] |
| 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 | O1O2O3U4O5O4U6U1O6U2U5U3 |
| R3 orbit | {'O1O2O3U4O5O4U6U1O6U2U5U3', 'O1O2O3U4O5O4U2U6U1O6U5U3'} |
| R3 orbit length | 2 |
| Gauss code of -K | O1O2O3U1U4U2O5U3U5O6O4U6 |
| Gauss code of K* | O1O2O3U4U1U3O5U2U5O6O4U6 |
| Gauss code of -K* | O1O2O3U4O5O4U6U2O6U1U3U5 |
| Diagrammatic symmetry type | c |
| Flat genus of the diagram | 2 |
| If K is checkerboard colorable | False |
| If K is almost classical | False |
| Based matrix from Gauss code | [[ 0 -2 -1 2 1 1 -1],[ 2 0 0 2 2 0 2],[ 1 0 0 2 1 0 1],[-2 -2 -2 0 -1 -1 -2],[-1 -2 -1 1 0 1 -2],[-1 0 0 1 -1 0 -1],[ 1 -2 -1 2 2 1 0]] |
| Primitive based matrix | [[ 0 2 1 1 -1 -1 -2],[-2 0 -1 -1 -2 -2 -2],[-1 1 0 1 -1 -2 -2],[-1 1 -1 0 0 -1 0],[ 1 2 1 0 0 1 0],[ 1 2 2 1 -1 0 -2],[ 2 2 2 0 0 2 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,-1,1,1,2,1,1,2,2,2,-1,1,2,2,0,1,0,-1,0,2] |
| Phi over symmetry | [-2,-1,-1,1,1,2,-1,1,1,3,2,1,0,1,1,1,2,1,-1,0,0] |
| Phi of -K | [-2,-1,-1,1,1,2,-1,1,1,3,2,1,0,1,1,1,2,1,-1,0,0] |
| Phi of K* | [-2,-1,-1,1,1,2,0,0,1,1,2,-1,1,2,3,0,1,1,-1,-1,1] |
| Phi of -K* | [-2,-1,-1,1,1,2,0,2,0,2,2,1,0,1,2,1,2,2,-1,1,1] |
| Symmetry type of based matrix | c |
| u-polynomial | 0 |
| Normalized Jones-Krushkal polynomial | 11z+23 |
| Enhanced Jones-Krushkal polynomial | 11w^2z+23w |
| Inner characteristic polynomial | t^6+30t^4+80t^2 |
| Outer characteristic polynomial | t^7+42t^5+124t^3 |
| Flat arrow polynomial | -8*K1**2 - 4*K1*K2 + 2*K1 + 4*K2 + 2*K3 + 5 |
| 2-strand cable arrow polynomial | -192*K1**6 - 192*K1**4*K2**2 + 544*K1**4*K2 - 1680*K1**4 + 384*K1**3*K2*K3 + 64*K1**3*K3*K4 - 1472*K1**2*K2**2 + 2272*K1**2*K2 - 528*K1**2*K3**2 - 112*K1**2*K4**2 - 692*K1**2 + 1728*K1*K2*K3 + 440*K1*K3*K4 + 80*K1*K4*K5 - 192*K2**4 - 96*K2**2*K3**2 - 16*K2**2*K4**2 + 184*K2**2*K4 - 1028*K2**2 + 112*K2*K3*K5 + 32*K2*K4*K6 - 608*K3**2 - 184*K4**2 - 52*K5**2 - 12*K6**2 + 1214 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{2, 6}, {3, 5}, {1, 4}], [{2, 6}, {3, 5}, {4}, {1}], [{4, 6}, {2, 5}, {1, 3}], [{5, 6}, {2, 4}, {1, 3}]] |
| If K is slice | False |