| Min(phi) over symmetries of the knot is: [-2,0,0,0,1,1,1,1,1,1,2,-1,0,0,1,0,1,0,1,1,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.1555'] |
| 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+17t^5+29t^3+6t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1555'] |
| 2-strand cable arrow polynomial of the knot is: 1280*K1**4*K2 - 4944*K1**4 + 896*K1**3*K2*K3 + 96*K1**3*K3*K4 - 1568*K1**3*K3 - 3728*K1**2*K2**2 - 1312*K1**2*K2*K4 + 7848*K1**2*K2 - 1264*K1**2*K3**2 - 304*K1**2*K4**2 - 3460*K1**2 + 64*K1*K2**3*K3 - 288*K1*K2**2*K3 - 64*K1*K2**2*K5 - 160*K1*K2*K3*K4 + 6392*K1*K2*K3 + 2384*K1*K3*K4 + 312*K1*K4*K5 - 72*K2**4 - 96*K2**2*K3**2 - 48*K2**2*K4**2 + 712*K2**2*K4 - 3396*K2**2 + 128*K2*K3*K5 + 32*K2*K4*K6 - 2128*K3**2 - 910*K4**2 - 84*K5**2 - 4*K6**2 + 3684 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1555'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.4652', 'vk6.4937', 'vk6.6096', 'vk6.6587', 'vk6.8113', 'vk6.8515', 'vk6.9503', 'vk6.9860', 'vk6.20626', 'vk6.22053', 'vk6.28112', 'vk6.29553', 'vk6.39528', 'vk6.41751', 'vk6.46139', 'vk6.47781', 'vk6.48684', 'vk6.48881', 'vk6.49430', 'vk6.49657', 'vk6.50698', 'vk6.50893', 'vk6.51181', 'vk6.51388', 'vk6.57510', 'vk6.58698', 'vk6.62206', 'vk6.63152', 'vk6.67020', 'vk6.67893', 'vk6.69649', 'vk6.70330'] |
| 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 | O1O2O3U4O5U3U2O4O6U5U1U6 |
| R3 orbit | {'O1O2O3U4O5U3U2O4O6U5U1U6'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U4U3U5O4O6U2U1O5U6 |
| Gauss code of K* | O1O2O3U2U4U5O6U1O5O4U6U3 |
| Gauss code of -K* | O1O2O3U1U4O5O6U3O4U6U5U2 |
| 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 0 0 0 1 2],[ 0 0 0 0 -1 1 1],[ 0 0 0 0 0 0 1],[ 1 0 1 0 0 0 1],[ 0 -1 -1 0 0 0 1],[-2 -2 -1 -1 -1 -1 0]] |
| Primitive based matrix | [[ 0 2 0 0 0 -1 -1],[-2 0 -1 -1 -1 -1 -2],[ 0 1 0 1 0 -1 0],[ 0 1 -1 0 0 0 -1],[ 0 1 0 0 0 0 0],[ 1 1 1 0 0 0 0],[ 1 2 0 1 0 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,0,0,0,1,1,1,1,1,1,2,-1,0,1,0,0,0,1,0,0,0] |
| Phi over symmetry | [-2,0,0,0,1,1,1,1,1,1,2,-1,0,0,1,0,1,0,1,1,0] |
| Phi of -K | [-1,-1,0,0,0,2,0,0,1,1,1,1,0,1,2,1,0,1,0,1,1] |
| Phi of K* | [-2,0,0,0,1,1,1,1,1,1,2,-1,0,0,1,0,1,0,1,1,0] |
| Phi of -K* | [-1,-1,0,0,0,2,0,0,0,1,1,0,1,0,2,0,0,1,-1,1,1] |
| Symmetry type of based matrix | c |
| u-polynomial | -t^2+2t |
| Normalized Jones-Krushkal polynomial | 4z^2+23z+31 |
| Enhanced Jones-Krushkal polynomial | 4w^3z^2+23w^2z+31w |
| Inner characteristic polynomial | t^6+11t^4+14t^2+1 |
| Outer characteristic polynomial | t^7+17t^5+29t^3+6t |
| Flat arrow polynomial | -2*K1**2 - 4*K1*K2 + 2*K1 + K2 + 2*K3 + 2 |
| 2-strand cable arrow polynomial | 1280*K1**4*K2 - 4944*K1**4 + 896*K1**3*K2*K3 + 96*K1**3*K3*K4 - 1568*K1**3*K3 - 3728*K1**2*K2**2 - 1312*K1**2*K2*K4 + 7848*K1**2*K2 - 1264*K1**2*K3**2 - 304*K1**2*K4**2 - 3460*K1**2 + 64*K1*K2**3*K3 - 288*K1*K2**2*K3 - 64*K1*K2**2*K5 - 160*K1*K2*K3*K4 + 6392*K1*K2*K3 + 2384*K1*K3*K4 + 312*K1*K4*K5 - 72*K2**4 - 96*K2**2*K3**2 - 48*K2**2*K4**2 + 712*K2**2*K4 - 3396*K2**2 + 128*K2*K3*K5 + 32*K2*K4*K6 - 2128*K3**2 - 910*K4**2 - 84*K5**2 - 4*K6**2 + 3684 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {2, 5}, {3, 4}], [{1, 6}, {3, 5}, {2, 4}], [{2, 6}, {3, 5}, {1, 4}], [{3, 6}, {2, 5}, {1, 4}], [{4, 6}, {2, 5}, {1, 3}], [{4, 6}, {3, 5}, {1, 2}], [{6}, {2, 5}, {3, 4}, {1}], [{6}, {3, 5}, {2, 4}, {1}]] |
| If K is slice | False |