| Min(phi) over symmetries of the knot is: [-3,-2,0,1,2,2,0,2,2,2,4,1,1,1,2,1,2,2,1,0,-2] |
| Flat knots (up to 7 crossings) with same phi are :['6.592'] |
| 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+71t^5+35t^3 |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.592'] |
| 2-strand cable arrow polynomial of the knot is: 64*K1**4*K2 - 448*K1**4 - 384*K1**2*K2**2 + 1320*K1**2*K2 - 64*K1**2*K3**2 - 1120*K1**2 + 840*K1*K2*K3 + 216*K1*K3*K4 - 40*K2**4 - 64*K2**2*K3**2 - 8*K2**2*K4**2 + 152*K2**2*K4 - 910*K2**2 + 80*K2*K3*K5 + 8*K2*K4*K6 - 416*K3**2 - 158*K4**2 - 24*K5**2 - 2*K6**2 + 956 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.592'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.71362', 'vk6.71421', 'vk6.71888', 'vk6.71947', 'vk6.72464', 'vk6.72613', 'vk6.72731', 'vk6.72825', 'vk6.72887', 'vk6.73045', 'vk6.73346', 'vk6.73509', 'vk6.74261', 'vk6.74385', 'vk6.74424', 'vk6.75038', 'vk6.75516', 'vk6.75831', 'vk6.76438', 'vk6.76609', 'vk6.77027', 'vk6.77768', 'vk6.77817', 'vk6.78236', 'vk6.78483', 'vk6.78628', 'vk6.78823', 'vk6.79313', 'vk6.79423', 'vk6.79841', 'vk6.79873', 'vk6.80262', 'vk6.80778', 'vk6.80873', 'vk6.85142', 'vk6.86529', 'vk6.87217', 'vk6.87341', 'vk6.89274', 'vk6.89443'] |
| 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 | O1O2O3O4U2O5U1O6U4U5U6U3 |
| R3 orbit | {'O1O2O3O4U2O5U1O6U4U5U6U3', 'O1O2O3O4U2O5U1U3O6U5U4U6'} |
| R3 orbit length | 2 |
| Gauss code of -K | O1O2O3O4U2U5U6U1O5U4O6U3 |
| Gauss code of K* | O1O2O3O4U5U6U4U1O6U2O5U3 |
| Gauss code of -K* | O1O2O3O4U2O5U3O6U4U1U6U5 |
| 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 -2 2 0 1 2],[ 3 0 0 4 2 2 2],[ 2 0 0 2 1 1 1],[-2 -4 -2 0 -2 0 2],[ 0 -2 -1 2 0 1 2],[-1 -2 -1 0 -1 0 1],[-2 -2 -1 -2 -2 -1 0]] |
| Primitive based matrix | [[ 0 2 2 1 0 -2 -3],[-2 0 2 0 -2 -2 -4],[-2 -2 0 -1 -2 -1 -2],[-1 0 1 0 -1 -1 -2],[ 0 2 2 1 0 -1 -2],[ 2 2 1 1 1 0 0],[ 3 4 2 2 2 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-2,-1,0,2,3,-2,0,2,2,4,1,2,1,2,1,1,2,1,2,0] |
| Phi over symmetry | [-3,-2,0,1,2,2,0,2,2,2,4,1,1,1,2,1,2,2,1,0,-2] |
| Phi of -K | [-3,-2,0,1,2,2,1,1,2,1,3,1,2,2,3,0,0,0,1,0,-2] |
| Phi of K* | [-2,-2,-1,0,2,3,-2,0,0,3,3,1,0,2,1,0,2,2,1,1,1] |
| Phi of -K* | [-3,-2,0,1,2,2,0,2,2,2,4,1,1,1,2,1,2,2,1,0,-2] |
| 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+49t^4 |
| Outer characteristic polynomial | t^7+71t^5+35t^3 |
| Flat arrow polynomial | -6*K1**2 - 2*K1*K2 + K1 + 3*K2 + K3 + 4 |
| 2-strand cable arrow polynomial | 64*K1**4*K2 - 448*K1**4 - 384*K1**2*K2**2 + 1320*K1**2*K2 - 64*K1**2*K3**2 - 1120*K1**2 + 840*K1*K2*K3 + 216*K1*K3*K4 - 40*K2**4 - 64*K2**2*K3**2 - 8*K2**2*K4**2 + 152*K2**2*K4 - 910*K2**2 + 80*K2*K3*K5 + 8*K2*K4*K6 - 416*K3**2 - 158*K4**2 - 24*K5**2 - 2*K6**2 + 956 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {2, 5}, {3, 4}], [{3, 6}, {1, 5}, {2, 4}], [{4, 6}, {3, 5}, {1, 2}], [{4, 6}, {5}, {3}, {1, 2}]] |
| If K is slice | False |