| Min(phi) over symmetries of the knot is: [-2,-2,0,1,1,2,-1,1,1,2,2,1,1,1,2,-1,0,0,-1,0,1] |
| Flat knots (up to 7 crossings) with same phi are :['6.1012'] |
| 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+49t^5+81t^3+19t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1012'] |
| 2-strand cable arrow polynomial of the knot is: -80*K1**4 + 32*K1**3*K2*K3 - 32*K1**3*K3 - 3008*K1**2*K2**2 - 320*K1**2*K2*K4 + 2552*K1**2*K2 - 144*K1**2*K3**2 - 3124*K1**2 + 672*K1*K2**3*K3 - 96*K1*K2**2*K3 - 32*K1*K2**2*K5 - 320*K1*K2*K3*K4 + 5840*K1*K2*K3 + 720*K1*K3*K4 + 64*K1*K4*K5 + 24*K1*K5*K6 - 424*K2**4 - 1104*K2**2*K3**2 - 112*K2**2*K4**2 + 512*K2**2*K4 - 2468*K2**2 + 736*K2*K3*K5 + 136*K2*K4*K6 - 2248*K3**2 - 414*K4**2 - 132*K5**2 - 52*K6**2 + 2820 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1012'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.71459', 'vk6.71512', 'vk6.71524', 'vk6.71981', 'vk6.71999', 'vk6.72038', 'vk6.72054', 'vk6.73224', 'vk6.73232', 'vk6.73255', 'vk6.73263', 'vk6.73658', 'vk6.73674', 'vk6.75151', 'vk6.75167', 'vk6.77080', 'vk6.77130', 'vk6.77140', 'vk6.77421', 'vk6.77435', 'vk6.78086', 'vk6.78092', 'vk6.78120', 'vk6.78126', 'vk6.81289', 'vk6.81536', 'vk6.81550', 'vk6.85481', 'vk6.85484', 'vk6.86887', 'vk6.87733', 'vk6.89501'] |
| 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 | O1O2O3O4U2U5O6U4O5U1U3U6 |
| R3 orbit | {'O1O2O3O4U2U5O6U4O5U1U3U6'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U5U2U4O6U1O5U6U3 |
| Gauss code of K* | O1O2O3U1U4U2U5O4O6U3O5U6 |
| Gauss code of -K* | O1O2O3U4O5U1O4O6U5U2U6U3 |
| 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 -2 1 1 0 2],[ 2 0 -1 2 2 1 2],[ 2 1 0 2 1 1 2],[-1 -2 -2 0 1 -2 1],[-1 -2 -1 -1 0 -1 0],[ 0 -1 -1 2 1 0 2],[-2 -2 -2 -1 0 -2 0]] |
| Primitive based matrix | [[ 0 2 1 1 0 -2 -2],[-2 0 0 -1 -2 -2 -2],[-1 0 0 -1 -1 -1 -2],[-1 1 1 0 -2 -2 -2],[ 0 2 1 2 0 -1 -1],[ 2 2 1 2 1 0 1],[ 2 2 2 2 1 -1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,-1,0,2,2,0,1,2,2,2,1,1,1,2,2,2,2,1,1,-1] |
| Phi over symmetry | [-2,-2,0,1,1,2,-1,1,1,2,2,1,1,1,2,-1,0,0,-1,0,1] |
| Phi of -K | [-2,-2,0,1,1,2,-1,1,1,2,2,1,1,1,2,-1,0,0,-1,0,1] |
| Phi of K* | [-2,-1,-1,0,2,2,0,1,0,2,2,1,-1,1,1,0,1,2,1,1,-1] |
| Phi of -K* | [-2,-2,0,1,1,2,-1,1,2,2,2,1,1,2,2,1,2,2,-1,0,1] |
| Symmetry type of based matrix | c |
| u-polynomial | t^2-2t |
| Normalized Jones-Krushkal polynomial | 3z^2+16z+21 |
| Enhanced Jones-Krushkal polynomial | 3w^3z^2-8w^3z+24w^2z+21w |
| Inner characteristic polynomial | t^6+35t^4+32t^2+4 |
| Outer characteristic polynomial | t^7+49t^5+81t^3+19t |
| Flat arrow polynomial | -2*K1**2 - 4*K1*K2 + 2*K1 + K2 + 2*K3 + 2 |
| 2-strand cable arrow polynomial | -80*K1**4 + 32*K1**3*K2*K3 - 32*K1**3*K3 - 3008*K1**2*K2**2 - 320*K1**2*K2*K4 + 2552*K1**2*K2 - 144*K1**2*K3**2 - 3124*K1**2 + 672*K1*K2**3*K3 - 96*K1*K2**2*K3 - 32*K1*K2**2*K5 - 320*K1*K2*K3*K4 + 5840*K1*K2*K3 + 720*K1*K3*K4 + 64*K1*K4*K5 + 24*K1*K5*K6 - 424*K2**4 - 1104*K2**2*K3**2 - 112*K2**2*K4**2 + 512*K2**2*K4 - 2468*K2**2 + 736*K2*K3*K5 + 136*K2*K4*K6 - 2248*K3**2 - 414*K4**2 - 132*K5**2 - 52*K6**2 + 2820 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{2, 6}, {1, 5}, {3, 4}], [{2, 6}, {3, 5}, {1, 4}], [{2, 6}, {4, 5}, {1, 3}], [{5, 6}, {2, 4}, {1, 3}]] |
| If K is slice | False |