| Min(phi) over symmetries of the knot is: [-2,0,0,0,1,1,0,1,2,0,1,0,-1,1,1,0,1,0,1,0,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.1762'] |
| 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+27t^5+73t^3+18t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1762'] |
| 2-strand cable arrow polynomial of the knot is: 224*K1**4*K2 - 1680*K1**4 + 352*K1**3*K2*K3 + 64*K1**3*K3*K4 - 1056*K1**3*K3 + 96*K1**2*K2**2*K4 - 2384*K1**2*K2**2 + 128*K1**2*K2*K3**2 - 544*K1**2*K2*K4 + 6824*K1**2*K2 - 624*K1**2*K3**2 - 176*K1**2*K4**2 - 5716*K1**2 + 64*K1*K2**3*K3 - 576*K1*K2**2*K3 - 160*K1*K2**2*K5 - 544*K1*K2*K3*K4 + 6144*K1*K2*K3 + 1504*K1*K3*K4 + 352*K1*K4*K5 - 104*K2**4 - 160*K2**2*K3**2 - 48*K2**2*K4**2 + 1232*K2**2*K4 - 4660*K2**2 + 344*K2*K3*K5 + 32*K2*K4*K6 - 2344*K3**2 - 942*K4**2 - 132*K5**2 - 4*K6**2 + 4492 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1762'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.16972', 'vk6.16978', 'vk6.17215', 'vk6.17221', 'vk6.20876', 'vk6.20881', 'vk6.22285', 'vk6.22288', 'vk6.23375', 'vk6.23677', 'vk6.23687', 'vk6.28351', 'vk6.35433', 'vk6.35867', 'vk6.35873', 'vk6.39979', 'vk6.39992', 'vk6.42051', 'vk6.43174', 'vk6.43176', 'vk6.46519', 'vk6.46532', 'vk6.55125', 'vk6.55139', 'vk6.55384', 'vk6.57675', 'vk6.57696', 'vk6.58873', 'vk6.59839', 'vk6.59865', 'vk6.68402', 'vk6.69739'] |
| 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 | O1O2O3U4U5O4O6U3U2O5U1U6 |
| R3 orbit | {'O1O2O3U4U5O4O6U3U2O5U1U6'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U4U3O5U2U1O4O6U5U6 |
| Gauss code of K* | O1O2U3O4O5U4U2U1O6O3U6U5 |
| Gauss code of -K* | O1O2U3O4O5U1U6O3O6U5U4U2 |
| 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 0 0 -1 0 2],[ 1 0 1 1 0 0 2],[ 0 -1 0 0 0 0 1],[ 0 -1 0 0 0 1 0],[ 1 0 0 0 0 0 3],[ 0 0 0 -1 0 0 2],[-2 -2 -1 0 -3 -2 0]] |
| Primitive based matrix | [[ 0 2 0 0 0 -1 -1],[-2 0 0 -1 -2 -2 -3],[ 0 0 0 0 1 -1 0],[ 0 1 0 0 0 -1 0],[ 0 2 -1 0 0 0 0],[ 1 2 1 1 0 0 0],[ 1 3 0 0 0 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,0,0,0,1,1,0,1,2,2,3,0,-1,1,0,0,1,0,0,0,0] |
| Phi over symmetry | [-2,0,0,0,1,1,0,1,2,0,1,0,-1,1,1,0,1,0,1,0,0] |
| Phi of -K | [-1,-1,0,0,0,2,0,0,0,1,1,1,1,1,0,0,-1,2,0,1,0] |
| Phi of K* | [-2,0,0,0,1,1,0,1,2,0,1,0,-1,1,1,0,1,0,1,0,0] |
| Phi of -K* | [-1,-1,0,0,0,2,0,0,0,0,3,0,1,1,2,-1,0,2,0,0,1] |
| 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+21t^4+50t^2+9 |
| Outer characteristic polynomial | t^7+27t^5+73t^3+18t |
| Flat arrow polynomial | -2*K1**2 - 4*K1*K2 + 2*K1 + K2 + 2*K3 + 2 |
| 2-strand cable arrow polynomial | 224*K1**4*K2 - 1680*K1**4 + 352*K1**3*K2*K3 + 64*K1**3*K3*K4 - 1056*K1**3*K3 + 96*K1**2*K2**2*K4 - 2384*K1**2*K2**2 + 128*K1**2*K2*K3**2 - 544*K1**2*K2*K4 + 6824*K1**2*K2 - 624*K1**2*K3**2 - 176*K1**2*K4**2 - 5716*K1**2 + 64*K1*K2**3*K3 - 576*K1*K2**2*K3 - 160*K1*K2**2*K5 - 544*K1*K2*K3*K4 + 6144*K1*K2*K3 + 1504*K1*K3*K4 + 352*K1*K4*K5 - 104*K2**4 - 160*K2**2*K3**2 - 48*K2**2*K4**2 + 1232*K2**2*K4 - 4660*K2**2 + 344*K2*K3*K5 + 32*K2*K4*K6 - 2344*K3**2 - 942*K4**2 - 132*K5**2 - 4*K6**2 + 4492 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {4, 5}, {2, 3}], [{1, 6}, {4, 5}, {3}, {2}], [{2, 6}, {4, 5}, {1, 3}], [{3, 6}, {4, 5}, {1, 2}], [{4, 6}, {1, 5}, {2, 3}], [{4, 6}, {1, 5}, {3}, {2}], [{5, 6}, {1, 4}, {2, 3}], [{5, 6}, {1, 4}, {3}, {2}]] |
| If K is slice | False |