| Min(phi) over symmetries of the knot is: [-2,-1,0,1,1,1,0,0,1,1,1,1,1,1,1,0,1,2,1,1,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.1933'] |
| Arrow polynomial of the knot is: -2*K1**2 + K2 + 2 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['4.6', '4.8', '6.780', '6.804', '6.914', '6.931', '6.946', '6.960', '6.1002', '6.1016', '6.1019', '6.1051', '6.1058', '6.1078', '6.1102', '6.1115', '6.1217', '6.1294', '6.1306', '6.1317', '6.1321', '6.1324', '6.1336', '6.1377', '6.1416', '6.1420', '6.1427', '6.1429', '6.1434', '6.1436', '6.1437', '6.1439', '6.1441', '6.1444', '6.1450', '6.1451', '6.1458', '6.1459', '6.1477', '6.1482', '6.1490', '6.1503', '6.1504', '6.1511', '6.1521', '6.1547', '6.1560', '6.1561', '6.1562', '6.1597', '6.1598', '6.1600', '6.1601', '6.1608', '6.1620', '6.1622', '6.1624', '6.1634', '6.1635', '6.1637', '6.1638', '6.1713', '6.1725', '6.1758', '6.1846', '6.1933', '6.1944', '6.1949', '6.1950', '6.1951'] |
| Outer characteristic polynomial of the knot is: t^7+32t^5+76t^3+8t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1933'] |
| 2-strand cable arrow polynomial of the knot is: -1664*K1**2*K2**4 + 3040*K1**2*K2**3 - 5088*K1**2*K2**2 - 128*K1**2*K2*K4 + 4176*K1**2*K2 - 3000*K1**2 - 256*K1*K2**4*K3 + 2240*K1*K2**3*K3 + 64*K1*K2**2*K3*K4 - 1824*K1*K2**2*K3 - 160*K1*K2**2*K5 - 64*K1*K2*K3*K4 + 4056*K1*K2*K3 + 432*K1*K3*K4 + 8*K1*K4*K5 - 128*K2**6 + 192*K2**4*K4 - 2488*K2**4 - 1344*K2**2*K3**2 - 32*K2**2*K4**2 + 1576*K2**2*K4 - 936*K2**2 + 584*K2*K3*K5 - 1000*K3**2 - 278*K4**2 - 72*K5**2 + 2092 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1933'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.17030', 'vk6.17271', 'vk6.20562', 'vk6.21965', 'vk6.23459', 'vk6.23754', 'vk6.28022', 'vk6.29484', 'vk6.35535', 'vk6.35983', 'vk6.39427', 'vk6.41621', 'vk6.42947', 'vk6.43240', 'vk6.46009', 'vk6.47681', 'vk6.55210', 'vk6.55443', 'vk6.57435', 'vk6.58604', 'vk6.59608', 'vk6.59925', 'vk6.62107', 'vk6.63079', 'vk6.65016', 'vk6.65221', 'vk6.66969', 'vk6.67829', 'vk6.68289', 'vk6.68440', 'vk6.69583', 'vk6.70278'] |
| 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 | O1O2O3U1U4U5O6O5O4U2U3U6 |
| R3 orbit | {'O1O2O3U1U4U5O6O5O4U2U3U6'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U2U1U4O5O6O4U3U5U6 |
| Gauss code of K* | O1O2O3U4U1U2O4O5O6U3U6U5 |
| Gauss code of -K* | O1O2O3U4U5U1O5O4O6U2U3U6 |
| 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 -2 -1 1 1 1 0],[ 2 0 1 2 2 2 2],[ 1 -1 0 1 1 1 0],[-1 -2 -1 0 -1 -1 -1],[-1 -2 -1 1 0 0 1],[-1 -2 -1 1 0 0 0],[ 0 -2 0 1 -1 0 0]] |
| Primitive based matrix | [[ 0 1 1 1 0 -1 -2],[-1 0 1 0 1 -1 -2],[-1 -1 0 -1 -1 -1 -2],[-1 0 1 0 0 -1 -2],[ 0 -1 1 0 0 0 -2],[ 1 1 1 1 0 0 -1],[ 2 2 2 2 2 1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-1,-1,-1,0,1,2,-1,0,-1,1,2,1,1,1,2,0,1,2,0,2,1] |
| Phi over symmetry | [-2,-1,0,1,1,1,0,0,1,1,1,1,1,1,1,0,1,2,1,1,0] |
| Phi of -K | [-2,-1,0,1,1,1,0,0,1,1,1,1,1,1,1,0,1,2,1,1,0] |
| Phi of K* | [-1,-1,-1,0,1,2,-1,-1,0,1,1,0,1,1,1,2,1,1,1,0,0] |
| Phi of -K* | [-2,-1,0,1,1,1,1,2,2,2,2,0,1,1,1,-1,0,1,0,1,1] |
| Symmetry type of based matrix | c |
| u-polynomial | t^2-2t |
| Normalized Jones-Krushkal polynomial | 6z^2+19z+15 |
| Enhanced Jones-Krushkal polynomial | -4w^4z^2+10w^3z^2-4w^3z+23w^2z+15w |
| Inner characteristic polynomial | t^6+24t^4+31t^2+1 |
| Outer characteristic polynomial | t^7+32t^5+76t^3+8t |
| Flat arrow polynomial | -2*K1**2 + K2 + 2 |
| 2-strand cable arrow polynomial | -1664*K1**2*K2**4 + 3040*K1**2*K2**3 - 5088*K1**2*K2**2 - 128*K1**2*K2*K4 + 4176*K1**2*K2 - 3000*K1**2 - 256*K1*K2**4*K3 + 2240*K1*K2**3*K3 + 64*K1*K2**2*K3*K4 - 1824*K1*K2**2*K3 - 160*K1*K2**2*K5 - 64*K1*K2*K3*K4 + 4056*K1*K2*K3 + 432*K1*K3*K4 + 8*K1*K4*K5 - 128*K2**6 + 192*K2**4*K4 - 2488*K2**4 - 1344*K2**2*K3**2 - 32*K2**2*K4**2 + 1576*K2**2*K4 - 936*K2**2 + 584*K2*K3*K5 - 1000*K3**2 - 278*K4**2 - 72*K5**2 + 2092 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {2, 5}, {3, 4}], [{3, 6}, {2, 5}, {1, 4}], [{4, 6}, {2, 5}, {1, 3}]] |
| If K is slice | False |