| Min(phi) over symmetries of the knot is: [-2,-2,0,1,1,2,0,1,0,1,2,1,0,2,3,1,-1,-1,0,-1,1] |
| Flat knots (up to 7 crossings) with same phi are :['6.1043'] |
| 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+61t^5+320t^3+10t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1043'] |
| 2-strand cable arrow polynomial of the knot is: 32*K1**4*K2 - 752*K1**4 + 576*K1**3*K2*K3 + 32*K1**3*K3*K4 - 1280*K1**3*K3 - 1072*K1**2*K2**2 + 256*K1**2*K2*K3**2 - 160*K1**2*K2*K4 + 5464*K1**2*K2 - 1776*K1**2*K3**2 - 128*K1**2*K3*K5 - 48*K1**2*K4**2 - 6068*K1**2 + 128*K1*K2**3*K3 - 992*K1*K2**2*K3 - 128*K1*K2*K3*K4 + 6808*K1*K2*K3 + 2024*K1*K3*K4 + 136*K1*K4*K5 - 72*K2**4 - 512*K2**2*K3**2 - 16*K2**2*K4**2 + 400*K2**2*K4 - 4084*K2**2 + 336*K2*K3*K5 + 32*K2*K4*K6 - 2792*K3**2 - 582*K4**2 - 84*K5**2 - 12*K6**2 + 4332 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1043'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.4639', 'vk6.4912', 'vk6.6073', 'vk6.6576', 'vk6.8100', 'vk6.8490', 'vk6.9480', 'vk6.9849', 'vk6.20629', 'vk6.22058', 'vk6.28115', 'vk6.29558', 'vk6.39539', 'vk6.41764', 'vk6.46150', 'vk6.47794', 'vk6.48679', 'vk6.48872', 'vk6.49423', 'vk6.49654', 'vk6.50693', 'vk6.50884', 'vk6.51174', 'vk6.51385', 'vk6.57529', 'vk6.58719', 'vk6.62225', 'vk6.63173', 'vk6.67031', 'vk6.67906', 'vk6.69660', 'vk6.70343'] |
| 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 | O1O2O3O4U5U6O5U1O6U2U4U3 |
| R3 orbit | {'O1O2O3O4U5U6O5U1O6U2U4U3'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U2U1U3O5U4O6U5U6 |
| Gauss code of K* | O1O2O3U4U1U3U2O5O6U5O4U6 |
| Gauss code of -K* | O1O2O3U4O5U6O4O6U2U1U3U5 |
| 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 2 2 -1 0],[ 2 0 0 2 1 2 3],[ 1 0 0 2 1 0 2],[-2 -2 -2 0 0 -3 -1],[-2 -1 -1 0 0 -3 -1],[ 1 -2 0 3 3 0 0],[ 0 -3 -2 1 1 0 0]] |
| Primitive based matrix | [[ 0 2 2 0 -1 -1 -2],[-2 0 0 -1 -1 -3 -1],[-2 0 0 -1 -2 -3 -2],[ 0 1 1 0 -2 0 -3],[ 1 1 2 2 0 0 0],[ 1 3 3 0 0 0 -2],[ 2 1 2 3 0 2 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-2,0,1,1,2,0,1,1,3,1,1,2,3,2,2,0,3,0,0,2] |
| Phi over symmetry | [-2,-2,0,1,1,2,0,1,0,1,2,1,0,2,3,1,-1,-1,0,-1,1] |
| Phi of -K | [-2,-1,-1,0,2,2,-1,1,-1,2,3,0,1,0,0,-1,1,2,1,1,0] |
| Phi of K* | [-2,-2,0,1,1,2,0,1,0,1,2,1,0,2,3,1,-1,-1,0,-1,1] |
| Phi of -K* | [-2,-1,-1,0,2,2,0,2,3,1,2,0,2,1,2,0,3,3,1,1,0] |
| Symmetry type of based matrix | c |
| u-polynomial | -t^2+2t |
| Normalized Jones-Krushkal polynomial | 5z^2+24z+29 |
| Enhanced Jones-Krushkal polynomial | 5w^3z^2-2w^3z+26w^2z+29w |
| Inner characteristic polynomial | t^6+47t^4+231t^2+1 |
| Outer characteristic polynomial | t^7+61t^5+320t^3+10t |
| Flat arrow polynomial | -2*K1**2 - 4*K1*K2 + 2*K1 + K2 + 2*K3 + 2 |
| 2-strand cable arrow polynomial | 32*K1**4*K2 - 752*K1**4 + 576*K1**3*K2*K3 + 32*K1**3*K3*K4 - 1280*K1**3*K3 - 1072*K1**2*K2**2 + 256*K1**2*K2*K3**2 - 160*K1**2*K2*K4 + 5464*K1**2*K2 - 1776*K1**2*K3**2 - 128*K1**2*K3*K5 - 48*K1**2*K4**2 - 6068*K1**2 + 128*K1*K2**3*K3 - 992*K1*K2**2*K3 - 128*K1*K2*K3*K4 + 6808*K1*K2*K3 + 2024*K1*K3*K4 + 136*K1*K4*K5 - 72*K2**4 - 512*K2**2*K3**2 - 16*K2**2*K4**2 + 400*K2**2*K4 - 4084*K2**2 + 336*K2*K3*K5 + 32*K2*K4*K6 - 2792*K3**2 - 582*K4**2 - 84*K5**2 - 12*K6**2 + 4332 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{2, 6}, {4, 5}, {1, 3}], [{4, 6}, {2, 5}, {1, 3}], [{5, 6}, {2, 4}, {1, 3}]] |
| If K is slice | False |