| Min(phi) over symmetries of the knot is: [-3,-1,0,1,1,2,0,2,1,2,3,1,0,1,1,1,1,2,-1,-1,1] |
| Flat knots (up to 7 crossings) with same phi are :['6.766'] |
| 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+46t^5+29t^3 |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.766'] |
| 2-strand cable arrow polynomial of the knot is: -64*K1**6 + 160*K1**4*K2 - 832*K1**4 + 32*K1**3*K2*K3 - 672*K1**2*K2**2 + 1352*K1**2*K2 - 384*K1**2*K3**2 - 48*K1**2*K4**2 - 560*K1**2 + 976*K1*K2*K3 + 328*K1*K3*K4 + 40*K1*K4*K5 - 56*K2**4 - 48*K2**2*K3**2 - 8*K2**2*K4**2 + 56*K2**2*K4 - 590*K2**2 + 40*K2*K3*K5 + 8*K2*K4*K6 - 304*K3**2 - 82*K4**2 - 16*K5**2 - 2*K6**2 + 672 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.766'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.11463', 'vk6.11466', 'vk6.11767', 'vk6.11771', 'vk6.12782', 'vk6.12784', 'vk6.13118', 'vk6.13121', 'vk6.19184', 'vk6.19190', 'vk6.19479', 'vk6.19485', 'vk6.22367', 'vk6.22369', 'vk6.22762', 'vk6.22764', 'vk6.25985', 'vk6.25989', 'vk6.28331', 'vk6.28339', 'vk6.31219', 'vk6.31223', 'vk6.31570', 'vk6.31574', 'vk6.34628', 'vk6.34629', 'vk6.34713', 'vk6.34715', 'vk6.35541', 'vk6.35543', 'vk6.35992', 'vk6.35994', 'vk6.39959', 'vk6.39967', 'vk6.40123', 'vk6.40127', 'vk6.42349', 'vk6.42350', 'vk6.43247', 'vk6.43249', 'vk6.44570', 'vk6.44578', 'vk6.46641', 'vk6.46643', 'vk6.52228', 'vk6.52231', 'vk6.59146', 'vk6.59148'] |
| 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 | O1O2O3O4U3O5U1U4U2O6U5U6 |
| R3 orbit | {'O1O2O3U2O4O5U1U3O6U5U6U4', 'O1O2O3O4U3O5U1U4U2O6U5U6', 'O1O2O3U2O4O5U1U3U4O6U5U6'} |
| R3 orbit length | 3 |
| Gauss code of -K | O1O2O3O4U5U6O5U3U1U4O6U2 |
| Gauss code of K* | O1O2O3U4O5O4U1U3U6U2O6U5 |
| Gauss code of -K* | O1O2O3U4O5U2U5U1U3O6O4U6 |
| 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 -3 0 -1 1 2 1],[ 3 0 2 0 2 3 1],[ 0 -2 0 -1 1 2 1],[ 1 0 1 0 1 1 0],[-1 -2 -1 -1 0 1 1],[-2 -3 -2 -1 -1 0 1],[-1 -1 -1 0 -1 -1 0]] |
| Primitive based matrix | [[ 0 2 1 1 0 -1 -3],[-2 0 1 -1 -2 -1 -3],[-1 -1 0 -1 -1 0 -1],[-1 1 1 0 -1 -1 -2],[ 0 2 1 1 0 -1 -2],[ 1 1 0 1 1 0 0],[ 3 3 1 2 2 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,-1,0,1,3,-1,1,2,1,3,1,1,0,1,1,1,2,1,2,0] |
| Phi over symmetry | [-3,-1,0,1,1,2,0,2,1,2,3,1,0,1,1,1,1,2,-1,-1,1] |
| Phi of -K | [-3,-1,0,1,1,2,2,1,2,3,2,0,1,2,2,0,0,0,-1,0,2] |
| Phi of K* | [-2,-1,-1,0,1,3,0,2,0,2,2,1,0,1,2,0,2,3,0,1,2] |
| Phi of -K* | [-3,-1,0,1,1,2,0,2,1,2,3,1,0,1,1,1,1,2,-1,-1,1] |
| Symmetry type of based matrix | c |
| u-polynomial | t^3-t^2-t |
| Normalized Jones-Krushkal polynomial | 9z+19 |
| Enhanced Jones-Krushkal polynomial | 9w^2z+19w |
| Inner characteristic polynomial | t^6+30t^4+8t^2 |
| Outer characteristic polynomial | t^7+46t^5+29t^3 |
| Flat arrow polynomial | -6*K1**2 - 2*K1*K2 + K1 + 3*K2 + K3 + 4 |
| 2-strand cable arrow polynomial | -64*K1**6 + 160*K1**4*K2 - 832*K1**4 + 32*K1**3*K2*K3 - 672*K1**2*K2**2 + 1352*K1**2*K2 - 384*K1**2*K3**2 - 48*K1**2*K4**2 - 560*K1**2 + 976*K1*K2*K3 + 328*K1*K3*K4 + 40*K1*K4*K5 - 56*K2**4 - 48*K2**2*K3**2 - 8*K2**2*K4**2 + 56*K2**2*K4 - 590*K2**2 + 40*K2*K3*K5 + 8*K2*K4*K6 - 304*K3**2 - 82*K4**2 - 16*K5**2 - 2*K6**2 + 672 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{2, 6}, {3, 5}, {1, 4}], [{2, 6}, {5}, {1, 4}, {3}], [{4, 6}, {3, 5}, {1, 2}], [{4, 6}, {5}, {3}, {1, 2}]] |
| If K is slice | False |