| Min(phi) over symmetries of the knot is: [-2,0,0,0,1,1,0,0,0,2,2,-1,-1,0,1,0,0,1,0,1,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.1873'] |
| Arrow polynomial of the knot is: 4*K1**3 - 10*K1**2 - 4*K1*K2 - K1 + 5*K2 + K3 + 6 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.241', '6.341', '6.542', '6.567', '6.699', '6.713', '6.771', '6.791', '6.1025', '6.1039', '6.1041', '6.1072', '6.1077', '6.1121', '6.1123', '6.1499', '6.1502', '6.1531', '6.1645', '6.1648', '6.1726', '6.1727', '6.1761', '6.1784', '6.1807', '6.1823', '6.1832', '6.1869', '6.1873', '6.1874'] |
| Outer characteristic polynomial of the knot is: t^7+19t^5+55t^3 |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1873'] |
| 2-strand cable arrow polynomial of the knot is: -192*K1**4*K2**2 + 672*K1**4*K2 - 1456*K1**4 + 416*K1**2*K2**3 - 2400*K1**2*K2**2 + 3704*K1**2*K2 - 112*K1**2*K3**2 - 2708*K1**2 + 160*K1*K2**3*K3 + 2720*K1*K2*K3 + 424*K1*K3*K4 - 32*K2**6 + 64*K2**4*K4 - 664*K2**4 - 368*K2**2*K3**2 - 48*K2**2*K4**2 + 592*K2**2*K4 - 2006*K2**2 + 232*K2*K3*K5 + 16*K2*K4*K6 - 1048*K3**2 - 378*K4**2 - 44*K5**2 - 2*K6**2 + 2456 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1873'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.71370', 'vk6.71429', 'vk6.71896', 'vk6.71955', 'vk6.72461', 'vk6.72597', 'vk6.72716', 'vk6.72821', 'vk6.72883', 'vk6.73029', 'vk6.74227', 'vk6.74371', 'vk6.74423', 'vk6.74857', 'vk6.75039', 'vk6.76608', 'vk6.76905', 'vk6.77035', 'vk6.77407', 'vk6.77772', 'vk6.77821', 'vk6.79279', 'vk6.79409', 'vk6.79754', 'vk6.79827', 'vk6.79874', 'vk6.80859', 'vk6.80901', 'vk6.81379', 'vk6.85501', 'vk6.87213', 'vk6.89266'] |
| 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 | O1O2O3U4U2O5U1O6O4U5U6U3 |
| R3 orbit | {'O1O2O3U4U2O5U1O6O4U5U6U3'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U1U4U5O6O4U3O5U2U6 |
| Gauss code of K* | O1O2O3U4U5U3O6O5U1O4U2U6 |
| Gauss code of -K* | O1O2O3U4U2O5U3O6O4U1U6U5 |
| 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 -1 0 2 0 -1 0],[ 1 0 0 2 0 0 0],[ 0 0 0 0 0 -1 -1],[-2 -2 0 0 0 -2 0],[ 0 0 0 0 0 -1 -1],[ 1 0 1 2 1 0 1],[ 0 0 1 0 1 -1 0]] |
| Primitive based matrix | [[ 0 2 0 0 0 -1 -1],[-2 0 0 0 0 -2 -2],[ 0 0 0 1 1 0 -1],[ 0 0 -1 0 0 0 -1],[ 0 0 -1 0 0 0 -1],[ 1 2 0 0 0 0 0],[ 1 2 1 1 1 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,0,0,0,1,1,0,0,0,2,2,-1,-1,0,1,0,0,1,0,1,0] |
| Phi over symmetry | [-2,0,0,0,1,1,0,0,0,2,2,-1,-1,0,1,0,0,1,0,1,0] |
| Phi of -K | [-1,-1,0,0,0,2,0,0,0,0,1,1,1,1,1,-1,-1,2,0,2,2] |
| Phi of K* | [-2,0,0,0,1,1,2,2,2,1,1,-1,0,0,1,1,0,1,0,1,0] |
| Phi of -K* | [-1,-1,0,0,0,2,0,0,0,0,2,1,1,1,2,-1,0,0,1,0,0] |
| Symmetry type of based matrix | c |
| u-polynomial | -t^2+2t |
| Normalized Jones-Krushkal polynomial | 13z+27 |
| Enhanced Jones-Krushkal polynomial | -2w^3z+15w^2z+27w |
| Inner characteristic polynomial | t^6+13t^4+28t^2 |
| Outer characteristic polynomial | t^7+19t^5+55t^3 |
| Flat arrow polynomial | 4*K1**3 - 10*K1**2 - 4*K1*K2 - K1 + 5*K2 + K3 + 6 |
| 2-strand cable arrow polynomial | -192*K1**4*K2**2 + 672*K1**4*K2 - 1456*K1**4 + 416*K1**2*K2**3 - 2400*K1**2*K2**2 + 3704*K1**2*K2 - 112*K1**2*K3**2 - 2708*K1**2 + 160*K1*K2**3*K3 + 2720*K1*K2*K3 + 424*K1*K3*K4 - 32*K2**6 + 64*K2**4*K4 - 664*K2**4 - 368*K2**2*K3**2 - 48*K2**2*K4**2 + 592*K2**2*K4 - 2006*K2**2 + 232*K2*K3*K5 + 16*K2*K4*K6 - 1048*K3**2 - 378*K4**2 - 44*K5**2 - 2*K6**2 + 2456 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {2, 5}, {3, 4}], [{1, 6}, {4, 5}, {2, 3}]] |
| If K is slice | False |