| Min(phi) over symmetries of the knot is: [-2,-1,0,1,1,1,0,1,1,3,3,2,1,0,1,0,0,0,-1,-1,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.1022'] |
| 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+26t^5+61t^3+7t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1022', '6.1444'] |
| 2-strand cable arrow polynomial of the knot is: 672*K1**4*K2 - 1744*K1**4 + 128*K1**3*K2*K3 + 96*K1**3*K3*K4 - 896*K1**3*K3 - 1872*K1**2*K2**2 - 896*K1**2*K2*K4 + 5968*K1**2*K2 - 528*K1**2*K3**2 - 96*K1**2*K3*K5 - 144*K1**2*K4**2 - 5500*K1**2 - 576*K1*K2**2*K3 - 32*K1*K2**2*K5 - 128*K1*K2*K3*K4 + 5440*K1*K2*K3 + 2256*K1*K3*K4 + 248*K1*K4*K5 - 136*K2**4 - 16*K2**2*K4**2 + 1128*K2**2*K4 - 4148*K2**2 + 80*K2*K3*K5 + 32*K2*K4*K6 - 2400*K3**2 - 1182*K4**2 - 76*K5**2 - 12*K6**2 + 4332 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1022'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.3638', 'vk6.3733', 'vk6.3924', 'vk6.4021', 'vk6.7060', 'vk6.7121', 'vk6.7296', 'vk6.7391', 'vk6.11386', 'vk6.12573', 'vk6.12684', 'vk6.19107', 'vk6.19152', 'vk6.19819', 'vk6.25716', 'vk6.25775', 'vk6.26256', 'vk6.26701', 'vk6.30994', 'vk6.31121', 'vk6.32178', 'vk6.37827', 'vk6.37882', 'vk6.44977', 'vk6.48266', 'vk6.48445', 'vk6.50020', 'vk6.50163', 'vk6.52145', 'vk6.63725', 'vk6.66200', 'vk6.66227'] |
| 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 | O1O2O3O4U3U2O5U4O6U5U1U6 |
| R3 orbit | {'O1O2O3O4U3U2O5U4O6U5U1U6'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U5U4U6O5U1O6U3U2 |
| Gauss code of K* | O1O2O3U2U4U5U6O5O4U1O6U3 |
| Gauss code of -K* | O1O2O3U1O4U3O5O6U4U6U5U2 |
| 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 -1 -1 -1 1 0 2],[ 1 0 -1 -1 1 1 2],[ 1 1 0 0 2 1 0],[ 1 1 0 0 1 1 0],[-1 -1 -2 -1 0 1 1],[ 0 -1 -1 -1 -1 0 1],[-2 -2 0 0 -1 -1 0]] |
| Primitive based matrix | [[ 0 2 1 0 -1 -1 -1],[-2 0 -1 -1 0 0 -2],[-1 1 0 1 -1 -2 -1],[ 0 1 -1 0 -1 -1 -1],[ 1 0 1 1 0 0 1],[ 1 0 2 1 0 0 1],[ 1 2 1 1 -1 -1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,0,1,1,1,1,1,0,0,2,-1,1,2,1,1,1,1,0,-1,-1] |
| Phi over symmetry | [-2,-1,0,1,1,1,0,1,1,3,3,2,1,0,1,0,0,0,-1,-1,0] |
| Phi of -K | [-1,-1,-1,0,1,2,-1,0,0,0,3,1,0,1,1,0,1,3,2,1,0] |
| Phi of K* | [-2,-1,0,1,1,1,0,1,1,3,3,2,1,0,1,0,0,0,-1,-1,0] |
| Phi of -K* | [-1,-1,-1,0,1,2,-1,-1,1,1,2,0,1,1,0,1,2,0,-1,1,1] |
| Symmetry type of based matrix | c |
| u-polynomial | -t^2+2t |
| Normalized Jones-Krushkal polynomial | 6z^2+27z+31 |
| Enhanced Jones-Krushkal polynomial | 6w^3z^2+27w^2z+31w |
| Inner characteristic polynomial | t^6+18t^4+20t^2+1 |
| Outer characteristic polynomial | t^7+26t^5+61t^3+7t |
| Flat arrow polynomial | -2*K1**2 - 4*K1*K2 + 2*K1 + K2 + 2*K3 + 2 |
| 2-strand cable arrow polynomial | 672*K1**4*K2 - 1744*K1**4 + 128*K1**3*K2*K3 + 96*K1**3*K3*K4 - 896*K1**3*K3 - 1872*K1**2*K2**2 - 896*K1**2*K2*K4 + 5968*K1**2*K2 - 528*K1**2*K3**2 - 96*K1**2*K3*K5 - 144*K1**2*K4**2 - 5500*K1**2 - 576*K1*K2**2*K3 - 32*K1*K2**2*K5 - 128*K1*K2*K3*K4 + 5440*K1*K2*K3 + 2256*K1*K3*K4 + 248*K1*K4*K5 - 136*K2**4 - 16*K2**2*K4**2 + 1128*K2**2*K4 - 4148*K2**2 + 80*K2*K3*K5 + 32*K2*K4*K6 - 2400*K3**2 - 1182*K4**2 - 76*K5**2 - 12*K6**2 + 4332 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{2, 6}, {3, 5}, {1, 4}], [{3, 6}, {2, 5}, {1, 4}], [{5, 6}, {1, 4}, {2, 3}]] |
| If K is slice | False |