| Min(phi) over symmetries of the knot is: [-3,-1,0,1,1,2,0,2,1,3,2,1,0,1,1,1,2,1,-1,0,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.1353'] |
| Arrow polynomial of the knot is: -6*K1**2 - 2*K1*K2 + K1 + 3*K2 + K3 + 4 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.323', '6.380', '6.444', '6.472', '6.523', '6.579', '6.592', '6.595', '6.609', '6.614', '6.620', '6.644', '6.648', '6.669', '6.671', '6.681', '6.693', '6.724', '6.725', '6.757', '6.766', '6.785', '6.786', '6.797', '6.798', '6.816', '6.833', '6.972', '6.978', '6.1056', '6.1064', '6.1066', '6.1087', '6.1094', '6.1273', '6.1277', '6.1282', '6.1295', '6.1300', '6.1313', '6.1344', '6.1353', '6.1354'] |
| Outer characteristic polynomial of the knot is: t^7+44t^5+73t^3+4t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1353'] |
| 2-strand cable arrow polynomial of the knot is: -64*K1**4*K2**2 + 288*K1**4*K2 - 1488*K1**4 + 96*K1**3*K2*K3 - 32*K1**3*K3 + 288*K1**2*K2**3 - 2560*K1**2*K2**2 + 64*K1**2*K2*K3**2 + 4496*K1**2*K2 - 496*K1**2*K3**2 - 2892*K1**2 - 896*K1*K2**2*K3 - 128*K1*K2*K3*K4 + 3648*K1*K2*K3 + 920*K1*K3*K4 + 112*K1*K4*K5 + 24*K1*K5*K6 - 600*K2**4 - 240*K2**2*K3**2 - 8*K2**2*K4**2 + 992*K2**2*K4 - 2566*K2**2 + 392*K2*K3*K5 + 16*K2*K4*K6 - 1352*K3**2 - 546*K4**2 - 180*K5**2 - 18*K6**2 + 2728 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1353'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.16525', 'vk6.16617', 'vk6.17510', 'vk6.17566', 'vk6.18863', 'vk6.18941', 'vk6.19210', 'vk6.19505', 'vk6.23049', 'vk6.24110', 'vk6.25493', 'vk6.25568', 'vk6.26021', 'vk6.26407', 'vk6.34928', 'vk6.35042', 'vk6.36297', 'vk6.36365', 'vk6.37594', 'vk6.37683', 'vk6.42498', 'vk6.42610', 'vk6.43478', 'vk6.44610', 'vk6.54768', 'vk6.54860', 'vk6.56442', 'vk6.56558', 'vk6.59289', 'vk6.60186', 'vk6.66102', 'vk6.66144'] |
| 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 | O1O2O3U2O4O5U1U3U5O6U4U6 |
| R3 orbit | {'O1O2O3U2O4O5U1U3U5O6U4U6'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U4U5O4U6U1U3O6O5U2 |
| Gauss code of K* | O1O2O3U4O5O4U1U6U2O6U5U3 |
| Gauss code of -K* | O1O2O3U1U4O5U2U5U3O6O4U6 |
| 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 -3 -1 0 1 2 1],[ 3 0 0 2 3 2 1],[ 1 0 0 1 1 1 0],[ 0 -2 -1 0 2 1 1],[-1 -3 -1 -2 0 0 1],[-2 -2 -1 -1 0 0 0],[-1 -1 0 -1 -1 0 0]] |
| Primitive based matrix | [[ 0 2 1 1 0 -1 -3],[-2 0 0 0 -1 -1 -2],[-1 0 0 1 -2 -1 -3],[-1 0 -1 0 -1 0 -1],[ 0 1 2 1 0 -1 -2],[ 1 1 1 0 1 0 0],[ 3 2 3 1 2 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,-1,0,1,3,0,0,1,1,2,-1,2,1,3,1,0,1,1,2,0] |
| Phi over symmetry | [-3,-1,0,1,1,2,0,2,1,3,2,1,0,1,1,1,2,1,-1,0,0] |
| Phi of -K | [-3,-1,0,1,1,2,2,1,1,3,3,0,1,2,2,-1,0,1,-1,1,1] |
| Phi of K* | [-2,-1,-1,0,1,3,1,1,1,2,3,-1,0,2,3,-1,1,1,0,1,2] |
| Phi of -K* | [-3,-1,0,1,1,2,0,2,1,3,2,1,0,1,1,1,2,1,-1,0,0] |
| Symmetry type of based matrix | c |
| u-polynomial | t^3-t^2-t |
| Normalized Jones-Krushkal polynomial | 3z^2+20z+29 |
| Enhanced Jones-Krushkal polynomial | 3w^3z^2+20w^2z+29w |
| Inner characteristic polynomial | t^6+28t^4+16t^2 |
| Outer characteristic polynomial | t^7+44t^5+73t^3+4t |
| Flat arrow polynomial | -6*K1**2 - 2*K1*K2 + K1 + 3*K2 + K3 + 4 |
| 2-strand cable arrow polynomial | -64*K1**4*K2**2 + 288*K1**4*K2 - 1488*K1**4 + 96*K1**3*K2*K3 - 32*K1**3*K3 + 288*K1**2*K2**3 - 2560*K1**2*K2**2 + 64*K1**2*K2*K3**2 + 4496*K1**2*K2 - 496*K1**2*K3**2 - 2892*K1**2 - 896*K1*K2**2*K3 - 128*K1*K2*K3*K4 + 3648*K1*K2*K3 + 920*K1*K3*K4 + 112*K1*K4*K5 + 24*K1*K5*K6 - 600*K2**4 - 240*K2**2*K3**2 - 8*K2**2*K4**2 + 992*K2**2*K4 - 2566*K2**2 + 392*K2*K3*K5 + 16*K2*K4*K6 - 1352*K3**2 - 546*K4**2 - 180*K5**2 - 18*K6**2 + 2728 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{2, 6}, {1, 5}, {3, 4}], [{2, 6}, {3, 5}, {1, 4}], [{2, 6}, {4, 5}, {1, 3}], [{4, 6}, {1, 5}, {2, 3}]] |
| If K is slice | False |