| Min(phi) over symmetries of the knot is: [-2,-2,0,1,1,2,0,1,1,1,1,1,1,2,2,1,1,2,-1,0,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.1195'] |
| Arrow polynomial of the knot is: 4*K1**3 - 2*K1**2 - 4*K1*K2 - K1 + K2 + K3 + 2 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.568', '6.806', '6.1000', '6.1049', '6.1081', '6.1101', '6.1112', '6.1122', '6.1193', '6.1195', '6.1208', '6.1235', '6.1263', '6.1517', '6.1528', '6.1537', '6.1542', '6.1545', '6.1558', '6.1569', '6.1575', '6.1644', '6.1650', '6.1681', '6.1692', '6.1702', '6.1706', '6.1728', '6.1734', '6.1739', '6.1799', '6.1813', '6.1820', '6.1834', '6.1840', '6.1851', '6.1861', '6.1878'] |
| Outer characteristic polynomial of the knot is: t^7+45t^5+70t^3+12t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1195'] |
| 2-strand cable arrow polynomial of the knot is: -576*K1**2*K2**4 + 736*K1**2*K2**3 + 128*K1**2*K2**2*K4 - 5424*K1**2*K2**2 + 32*K1**2*K2*K3*K5 - 256*K1**2*K2*K4 + 5232*K1**2*K2 - 64*K1**2*K3**2 - 64*K1**2*K4**2 - 64*K1**2*K5**2 - 4368*K1**2 + 1152*K1*K2**3*K3 - 1056*K1*K2**2*K3 - 896*K1*K2**2*K5 - 352*K1*K2*K3*K4 + 6616*K1*K2*K3 - 96*K1*K2*K4*K5 + 688*K1*K3*K4 + 536*K1*K4*K5 + 120*K1*K5*K6 - 32*K2**6 + 64*K2**4*K4 - 1272*K2**4 - 32*K2**3*K6 - 624*K2**2*K3**2 - 80*K2**2*K4**2 + 1976*K2**2*K4 - 3630*K2**2 + 1200*K2*K3*K5 + 144*K2*K4*K6 - 2080*K3**2 - 786*K4**2 - 520*K5**2 - 74*K6**2 + 3720 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1195'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.4736', 'vk6.5060', 'vk6.6268', 'vk6.6711', 'vk6.8237', 'vk6.8684', 'vk6.9626', 'vk6.9944', 'vk6.20649', 'vk6.22082', 'vk6.28139', 'vk6.29570', 'vk6.39573', 'vk6.41806', 'vk6.46192', 'vk6.47812', 'vk6.48776', 'vk6.48986', 'vk6.49584', 'vk6.49789', 'vk6.50790', 'vk6.51005', 'vk6.51278', 'vk6.51474', 'vk6.57557', 'vk6.58729', 'vk6.62235', 'vk6.63183', 'vk6.67035', 'vk6.67910', 'vk6.69664', 'vk6.70347'] |
| 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 | O1O2O3O4U2U1U5O6O5U4U6U3 |
| R3 orbit | {'O1O2O3O4U2U1U5O6O5U4U6U3'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U2U5U1O6O5U6U4U3 |
| Gauss code of K* | O1O2O3U4U3O5O4O6U2U1U6U5 |
| Gauss code of -K* | O1O2O3U4U2O4O5O6U3U1U6U5 |
| 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 2 1 1 0],[ 2 0 0 3 2 2 1],[ 2 0 0 2 1 2 1],[-2 -3 -2 0 -1 -1 0],[-1 -2 -1 1 0 -1 0],[-1 -2 -2 1 1 0 0],[ 0 -1 -1 0 0 0 0]] |
| Primitive based matrix | [[ 0 2 1 1 0 -2 -2],[-2 0 -1 -1 0 -2 -3],[-1 1 0 1 0 -2 -2],[-1 1 -1 0 0 -1 -2],[ 0 0 0 0 0 -1 -1],[ 2 2 2 1 1 0 0],[ 2 3 2 2 1 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,-1,0,2,2,1,1,0,2,3,-1,0,2,2,0,1,2,1,1,0] |
| Phi over symmetry | [-2,-2,0,1,1,2,0,1,1,1,1,1,1,2,2,1,1,2,-1,0,0] |
| Phi of -K | [-2,-2,0,1,1,2,0,1,1,1,1,1,1,2,2,1,1,2,-1,0,0] |
| Phi of K* | [-2,-1,-1,0,2,2,0,0,2,1,2,-1,1,1,2,1,1,1,1,1,0] |
| Phi of -K* | [-2,-2,0,1,1,2,0,1,1,2,2,1,2,2,3,0,0,0,-1,1,1] |
| Symmetry type of based matrix | c |
| u-polynomial | t^2-2t |
| Normalized Jones-Krushkal polynomial | 7z^2+24z+21 |
| Enhanced Jones-Krushkal polynomial | 7w^3z^2-4w^3z+28w^2z+21w |
| Inner characteristic polynomial | t^6+31t^4+35t^2 |
| Outer characteristic polynomial | t^7+45t^5+70t^3+12t |
| Flat arrow polynomial | 4*K1**3 - 2*K1**2 - 4*K1*K2 - K1 + K2 + K3 + 2 |
| 2-strand cable arrow polynomial | -576*K1**2*K2**4 + 736*K1**2*K2**3 + 128*K1**2*K2**2*K4 - 5424*K1**2*K2**2 + 32*K1**2*K2*K3*K5 - 256*K1**2*K2*K4 + 5232*K1**2*K2 - 64*K1**2*K3**2 - 64*K1**2*K4**2 - 64*K1**2*K5**2 - 4368*K1**2 + 1152*K1*K2**3*K3 - 1056*K1*K2**2*K3 - 896*K1*K2**2*K5 - 352*K1*K2*K3*K4 + 6616*K1*K2*K3 - 96*K1*K2*K4*K5 + 688*K1*K3*K4 + 536*K1*K4*K5 + 120*K1*K5*K6 - 32*K2**6 + 64*K2**4*K4 - 1272*K2**4 - 32*K2**3*K6 - 624*K2**2*K3**2 - 80*K2**2*K4**2 + 1976*K2**2*K4 - 3630*K2**2 + 1200*K2*K3*K5 + 144*K2*K4*K6 - 2080*K3**2 - 786*K4**2 - 520*K5**2 - 74*K6**2 + 3720 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {3, 5}, {2, 4}]] |
| If K is slice | False |