| Min(phi) over symmetries of the knot is: [-3,-2,-2,2,2,3,-1,1,2,4,4,1,1,2,2,1,2,3,0,0,1] |
| Flat knots (up to 7 crossings) with same phi are :['6.337'] |
| Arrow polynomial of the knot is: 4*K1**3 - 8*K1**2 - 4*K1*K2 - K1 + 4*K2 + K3 + 5 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.315', '6.337', '6.389', '6.418', '6.599', '6.675', '6.686', '6.688', '6.746', '6.747', '6.809', '6.1034', '6.1128', '6.1133', '6.1334', '6.1363', '6.1489', '6.1539', '6.1564', '6.1821', '6.1863'] |
| Outer characteristic polynomial of the knot is: t^7+97t^5+111t^3+4t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.337'] |
| 2-strand cable arrow polynomial of the knot is: -560*K1**4 + 32*K1**3*K2*K3 - 160*K1**3*K3 - 256*K1**2*K2**4 + 672*K1**2*K2**3 + 96*K1**2*K2**2*K4 - 2944*K1**2*K2**2 + 32*K1**2*K2*K3**2 - 160*K1**2*K2*K4 + 6056*K1**2*K2 - 208*K1**2*K3**2 - 32*K1**2*K4**2 - 5144*K1**2 + 544*K1*K2**3*K3 - 1504*K1*K2**2*K3 - 224*K1*K2**2*K5 - 96*K1*K2*K3*K4 + 4560*K1*K2*K3 + 840*K1*K3*K4 + 128*K1*K4*K5 + 8*K1*K5*K6 - 32*K2**6 + 32*K2**4*K4 - 768*K2**4 - 256*K2**2*K3**2 - 16*K2**2*K4**2 + 1200*K2**2*K4 - 3518*K2**2 + 256*K2*K3*K5 + 16*K2*K4*K6 - 1568*K3**2 - 488*K4**2 - 112*K5**2 - 10*K6**2 + 3582 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.337'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.73366', 'vk6.73380', 'vk6.73529', 'vk6.73557', 'vk6.73734', 'vk6.73853', 'vk6.74246', 'vk6.74874', 'vk6.75319', 'vk6.75538', 'vk6.75851', 'vk6.76423', 'vk6.78250', 'vk6.78301', 'vk6.78501', 'vk6.78650', 'vk6.78845', 'vk6.79294', 'vk6.80072', 'vk6.80087', 'vk6.80221', 'vk6.80276', 'vk6.80408', 'vk6.80759', 'vk6.81947', 'vk6.82674', 'vk6.84742', 'vk6.85038', 'vk6.85159', 'vk6.86518', 'vk6.87349', 'vk6.89428'] |
| 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 | O1O2O3O4O5U3U1O6U2U5U6U4 |
| R3 orbit | {'O1O2O3O4O5U3U1O6U2U5U6U4'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4O5U2U6U1U4O6U5U3 |
| Gauss code of K* | O1O2O3O4U5U1U6U4U2O6O5U3 |
| Gauss code of -K* | O1O2O3O4U2O5O6U3U1U6U4U5 |
| 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 -3 -2 -2 3 2 2],[ 3 0 1 0 4 3 2],[ 2 -1 0 0 4 2 2],[ 2 0 0 0 2 1 1],[-3 -4 -4 -2 0 -1 1],[-2 -3 -2 -1 1 0 1],[-2 -2 -2 -1 -1 -1 0]] |
| Primitive based matrix | [[ 0 3 2 2 -2 -2 -3],[-3 0 1 -1 -2 -4 -4],[-2 -1 0 -1 -1 -2 -2],[-2 1 1 0 -1 -2 -3],[ 2 2 1 1 0 0 0],[ 2 4 2 2 0 0 -1],[ 3 4 2 3 0 1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-3,-2,-2,2,2,3,-1,1,2,4,4,1,1,2,2,1,2,3,0,0,1] |
| Phi over symmetry | [-3,-2,-2,2,2,3,-1,1,2,4,4,1,1,2,2,1,2,3,0,0,1] |
| Phi of -K | [-3,-2,-2,2,2,3,0,1,2,3,2,0,2,2,1,3,3,3,-1,0,2] |
| Phi of K* | [-3,-2,-2,2,2,3,0,2,1,3,2,1,2,3,2,2,3,3,0,0,1] |
| Phi of -K* | [-3,-2,-2,2,2,3,0,1,2,3,4,0,1,1,2,2,2,4,-1,-1,1] |
| Symmetry type of based matrix | c |
| u-polynomial | 0 |
| Normalized Jones-Krushkal polynomial | 3z^2+20z+29 |
| Enhanced Jones-Krushkal polynomial | 3w^3z^2+20w^2z+29w |
| Inner characteristic polynomial | t^6+63t^4+23t^2 |
| Outer characteristic polynomial | t^7+97t^5+111t^3+4t |
| Flat arrow polynomial | 4*K1**3 - 8*K1**2 - 4*K1*K2 - K1 + 4*K2 + K3 + 5 |
| 2-strand cable arrow polynomial | -560*K1**4 + 32*K1**3*K2*K3 - 160*K1**3*K3 - 256*K1**2*K2**4 + 672*K1**2*K2**3 + 96*K1**2*K2**2*K4 - 2944*K1**2*K2**2 + 32*K1**2*K2*K3**2 - 160*K1**2*K2*K4 + 6056*K1**2*K2 - 208*K1**2*K3**2 - 32*K1**2*K4**2 - 5144*K1**2 + 544*K1*K2**3*K3 - 1504*K1*K2**2*K3 - 224*K1*K2**2*K5 - 96*K1*K2*K3*K4 + 4560*K1*K2*K3 + 840*K1*K3*K4 + 128*K1*K4*K5 + 8*K1*K5*K6 - 32*K2**6 + 32*K2**4*K4 - 768*K2**4 - 256*K2**2*K3**2 - 16*K2**2*K4**2 + 1200*K2**2*K4 - 3518*K2**2 + 256*K2*K3*K5 + 16*K2*K4*K6 - 1568*K3**2 - 488*K4**2 - 112*K5**2 - 10*K6**2 + 3582 |
| Genus of based matrix | 0 |
| Fillings of based matrix | [[{2, 6}, {3, 5}, {1, 4}]] |
| If K is slice | True |