| Min(phi) over symmetries of the knot is: [-3,-2,0,1,1,3,0,2,1,2,4,1,0,1,2,1,1,2,0,-1,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.320'] |
| Arrow polynomial of the knot is: -2*K1**2 - 4*K1*K2 + 2*K1 + K2 + 2*K3 + 2 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.120', '6.213', '6.216', '6.320', '6.322', '6.615', '6.617', '6.891', '6.951', '6.955', '6.1001', '6.1012', '6.1022', '6.1043', '6.1047', '6.1063', '6.1074', '6.1249', '6.1544', '6.1546', '6.1555', '6.1573', '6.1574', '6.1585', '6.1756', '6.1757', '6.1762', '6.1802', '6.1803', '6.1824', '6.1881', '6.1935'] |
| Outer characteristic polynomial of the knot is: t^7+80t^5+29t^3 |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.320'] |
| 2-strand cable arrow polynomial of the knot is: -48*K1**2*K2**2 + 104*K1**2*K2 - 432*K1**2*K3**2 - 756*K1**2 + 32*K1*K2*K3**3 + 1248*K1*K2*K3 + 536*K1*K3*K4 + 8*K1*K4*K5 + 24*K1*K5*K6 - 8*K2**4 - 64*K2**2*K3**2 - 16*K2**2*K4**2 + 136*K2**2*K4 - 680*K2**2 + 56*K2*K3*K5 + 24*K2*K4*K6 - 48*K3**4 + 24*K3**2*K6 - 652*K3**2 - 238*K4**2 - 32*K5**2 - 24*K6**2 + 804 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.320'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.11449', 'vk6.11744', 'vk6.12759', 'vk6.13102', 'vk6.20327', 'vk6.21668', 'vk6.27627', 'vk6.29171', 'vk6.31200', 'vk6.31539', 'vk6.32364', 'vk6.32779', 'vk6.39051', 'vk6.41311', 'vk6.45803', 'vk6.47478', 'vk6.52202', 'vk6.52463', 'vk6.53029', 'vk6.53349', 'vk6.57186', 'vk6.58397', 'vk6.61796', 'vk6.62917', 'vk6.63768', 'vk6.63878', 'vk6.64192', 'vk6.64378', 'vk6.66795', 'vk6.67663', 'vk6.69431', 'vk6.70153', 'vk6.82005', 'vk6.82738', 'vk6.84322', 'vk6.85655', 'vk6.86547', 'vk6.87578', 'vk6.88264', 'vk6.89417'] |
| 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 | O1O2O3O4O5U2U4O6U3U5U1U6 |
| R3 orbit | {'O1O2O3O4O5U2U4O6U3U5U1U6', 'O1O2O3O4U1O5U4O6U3U2U5U6'} |
| R3 orbit length | 2 |
| Gauss code of -K | O1O2O3O4O5U6U5U1U3O6U2U4 |
| Gauss code of K* | O1O2O3O4U3U5U1U6U2O5O6U4 |
| Gauss code of -K* | O1O2O3O4U1O5O6U3U5U4U6U2 |
| 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 -3 -1 0 2 3],[ 1 0 -3 0 0 3 3],[ 3 3 0 2 1 3 2],[ 1 0 -2 0 0 2 2],[ 0 0 -1 0 0 1 1],[-2 -3 -3 -2 -1 0 1],[-3 -3 -2 -2 -1 -1 0]] |
| Primitive based matrix | [[ 0 3 2 0 -1 -1 -3],[-3 0 -1 -1 -2 -3 -2],[-2 1 0 -1 -2 -3 -3],[ 0 1 1 0 0 0 -1],[ 1 2 2 0 0 0 -2],[ 1 3 3 0 0 0 -3],[ 3 2 3 1 2 3 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-3,-2,0,1,1,3,1,1,2,3,2,1,2,3,3,0,0,1,0,2,3] |
| Phi over symmetry | [-3,-2,0,1,1,3,0,2,1,2,4,1,0,1,2,1,1,2,0,-1,0] |
| Phi of -K | [-3,-1,-1,0,2,3,-1,0,2,2,4,0,1,0,1,1,1,2,1,2,0] |
| Phi of K* | [-3,-2,0,1,1,3,0,2,1,2,4,1,0,1,2,1,1,2,0,-1,0] |
| Phi of -K* | [-3,-1,-1,0,2,3,2,3,1,3,2,0,0,2,2,0,3,3,1,1,1] |
| Symmetry type of based matrix | c |
| u-polynomial | -t^2+2t |
| Normalized Jones-Krushkal polynomial | 7z+15 |
| Enhanced Jones-Krushkal polynomial | -4w^3z+11w^2z+15w |
| Inner characteristic polynomial | t^6+56t^4 |
| Outer characteristic polynomial | t^7+80t^5+29t^3 |
| Flat arrow polynomial | -2*K1**2 - 4*K1*K2 + 2*K1 + K2 + 2*K3 + 2 |
| 2-strand cable arrow polynomial | -48*K1**2*K2**2 + 104*K1**2*K2 - 432*K1**2*K3**2 - 756*K1**2 + 32*K1*K2*K3**3 + 1248*K1*K2*K3 + 536*K1*K3*K4 + 8*K1*K4*K5 + 24*K1*K5*K6 - 8*K2**4 - 64*K2**2*K3**2 - 16*K2**2*K4**2 + 136*K2**2*K4 - 680*K2**2 + 56*K2*K3*K5 + 24*K2*K4*K6 - 48*K3**4 + 24*K3**2*K6 - 652*K3**2 - 238*K4**2 - 32*K5**2 - 24*K6**2 + 804 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {2, 5}, {3, 4}], [{3, 6}, {4, 5}, {1, 2}], [{6}, {2, 5}, {3, 4}, {1}]] |
| If K is slice | False |