| Min(phi) over symmetries of the knot is: [-2,-1,0,0,1,2,-1,0,1,2,2,0,0,2,1,0,1,1,1,1,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.1539'] |
| 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+33t^5+53t^3+9t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1539'] |
| 2-strand cable arrow polynomial of the knot is: -192*K1**4*K2**2 + 384*K1**4*K2 - 1408*K1**4 + 128*K1**3*K2*K3 - 352*K1**3*K3 - 384*K1**2*K2**4 + 2656*K1**2*K2**3 - 6912*K1**2*K2**2 + 64*K1**2*K2*K3**2 - 480*K1**2*K2*K4 + 7824*K1**2*K2 - 224*K1**2*K3**2 - 5252*K1**2 - 384*K1*K2**4*K3 + 1312*K1*K2**3*K3 + 96*K1*K2**2*K3*K4 - 1408*K1*K2**2*K3 - 96*K1*K2**2*K5 - 320*K1*K2*K3*K4 + 6432*K1*K2*K3 + 688*K1*K3*K4 + 16*K1*K4*K5 - 288*K2**6 + 448*K2**4*K4 - 2480*K2**4 - 32*K2**3*K6 - 880*K2**2*K3**2 - 112*K2**2*K4**2 + 1720*K2**2*K4 - 2734*K2**2 + 416*K2*K3*K5 + 24*K2*K4*K6 - 1696*K3**2 - 404*K4**2 - 28*K5**2 - 2*K6**2 + 3858 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1539'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.73709', 'vk6.73826', 'vk6.74190', 'vk6.74800', 'vk6.75638', 'vk6.75822', 'vk6.76351', 'vk6.76869', 'vk6.78621', 'vk6.78814', 'vk6.79219', 'vk6.79688', 'vk6.80255', 'vk6.80391', 'vk6.80692', 'vk6.81064', 'vk6.81614', 'vk6.81792', 'vk6.81924', 'vk6.82173', 'vk6.82300', 'vk6.82648', 'vk6.83202', 'vk6.84062', 'vk6.84222', 'vk6.84688', 'vk6.85008', 'vk6.86012', 'vk6.87758', 'vk6.88218', 'vk6.89395', 'vk6.89610'] |
| 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 | O1O2O3U4O5U1U2O4O6U5U3U6 |
| R3 orbit | {'O1O2O3U4O5U1U2O4O6U5U3U6'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U4U1U5O4O6U2U3O5U6 |
| Gauss code of K* | O1O2O3U4U5U2O6U1O4O5U6U3 |
| Gauss code of -K* | O1O2O3U1U4O5O6U3O4U2U5U6 |
| 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 0 1 -1 0 2],[ 2 0 1 2 1 1 2],[ 0 -1 0 1 0 0 2],[-1 -2 -1 0 0 -1 2],[ 1 -1 0 0 0 0 1],[ 0 -1 0 1 0 0 1],[-2 -2 -2 -2 -1 -1 0]] |
| Primitive based matrix | [[ 0 2 1 0 0 -1 -2],[-2 0 -2 -1 -2 -1 -2],[-1 2 0 -1 -1 0 -2],[ 0 1 1 0 0 0 -1],[ 0 2 1 0 0 0 -1],[ 1 1 0 0 0 0 -1],[ 2 2 2 1 1 1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,0,0,1,2,2,1,2,1,2,1,1,0,2,0,0,1,0,1,1] |
| Phi over symmetry | [-2,-1,0,0,1,2,-1,0,1,2,2,0,0,2,1,0,1,1,1,1,0] |
| Phi of -K | [-2,-1,0,0,1,2,0,1,1,1,2,1,1,2,2,0,0,0,0,1,-1] |
| Phi of K* | [-2,-1,0,0,1,2,-1,0,1,2,2,0,0,2,1,0,1,1,1,1,0] |
| Phi of -K* | [-2,-1,0,0,1,2,1,1,1,2,2,0,0,0,1,0,1,1,1,2,2] |
| Symmetry type of based matrix | c |
| u-polynomial | 0 |
| Normalized Jones-Krushkal polynomial | 4z^2+21z+27 |
| Enhanced Jones-Krushkal polynomial | -2w^4z^2+6w^3z^2-2w^3z+23w^2z+27w |
| Inner characteristic polynomial | t^6+23t^4+11t^2+1 |
| Outer characteristic polynomial | t^7+33t^5+53t^3+9t |
| Flat arrow polynomial | 4*K1**3 - 8*K1**2 - 4*K1*K2 - K1 + 4*K2 + K3 + 5 |
| 2-strand cable arrow polynomial | -192*K1**4*K2**2 + 384*K1**4*K2 - 1408*K1**4 + 128*K1**3*K2*K3 - 352*K1**3*K3 - 384*K1**2*K2**4 + 2656*K1**2*K2**3 - 6912*K1**2*K2**2 + 64*K1**2*K2*K3**2 - 480*K1**2*K2*K4 + 7824*K1**2*K2 - 224*K1**2*K3**2 - 5252*K1**2 - 384*K1*K2**4*K3 + 1312*K1*K2**3*K3 + 96*K1*K2**2*K3*K4 - 1408*K1*K2**2*K3 - 96*K1*K2**2*K5 - 320*K1*K2*K3*K4 + 6432*K1*K2*K3 + 688*K1*K3*K4 + 16*K1*K4*K5 - 288*K2**6 + 448*K2**4*K4 - 2480*K2**4 - 32*K2**3*K6 - 880*K2**2*K3**2 - 112*K2**2*K4**2 + 1720*K2**2*K4 - 2734*K2**2 + 416*K2*K3*K5 + 24*K2*K4*K6 - 1696*K3**2 - 404*K4**2 - 28*K5**2 - 2*K6**2 + 3858 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {2, 5}, {3, 4}]] |
| If K is slice | False |