| Min(phi) over symmetries of the knot is: [-2,-2,-1,1,2,2,0,-1,1,3,4,0,0,1,2,1,1,1,0,0,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.774'] |
| Arrow polynomial of the knot is: 4*K1**3 - 4*K1*K2 - K1 + K3 + 1 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.395', '6.430', '6.440', '6.548', '6.551', '6.774', '6.832', '6.887', '6.908', '6.911', '6.1205', '6.1332', '6.1339', '6.1341', '6.1346', '6.1382', '6.1488', '6.1651', '6.1655', '6.1686'] |
| Outer characteristic polynomial of the knot is: t^7+53t^5+104t^3+11t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.774'] |
| 2-strand cable arrow polynomial of the knot is: 1504*K1**4*K2 - 2656*K1**4 + 928*K1**3*K2*K3 - 832*K1**3*K3 - 128*K1**2*K2**4 + 544*K1**2*K2**3 + 128*K1**2*K2**2*K4 - 6160*K1**2*K2**2 - 352*K1**2*K2*K4 + 6320*K1**2*K2 - 928*K1**2*K3**2 - 32*K1**2*K4**2 - 2912*K1**2 + 416*K1*K2**3*K3 - 1056*K1*K2**2*K3 - 160*K1*K2**2*K5 - 32*K1*K2*K3*K4 + 6312*K1*K2*K3 + 792*K1*K3*K4 + 32*K1*K4*K5 - 32*K2**6 + 64*K2**4*K4 - 800*K2**4 - 32*K2**3*K6 - 272*K2**2*K3**2 - 16*K2**2*K4**2 + 720*K2**2*K4 - 2446*K2**2 + 104*K2*K3*K5 + 16*K2*K4*K6 - 1556*K3**2 - 172*K4**2 - 4*K5**2 - 2*K6**2 + 2698 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.774'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.16808', 'vk6.16812', 'vk6.16865', 'vk6.16869', 'vk6.18171', 'vk6.18173', 'vk6.18508', 'vk6.18510', 'vk6.23248', 'vk6.23252', 'vk6.24627', 'vk6.25049', 'vk6.25051', 'vk6.35241', 'vk6.35271', 'vk6.36766', 'vk6.37199', 'vk6.37201', 'vk6.42763', 'vk6.42767', 'vk6.44347', 'vk6.44349', 'vk6.55003', 'vk6.55035', 'vk6.55976', 'vk6.55978', 'vk6.59406', 'vk6.59410', 'vk6.60511', 'vk6.65643', 'vk6.68189', 'vk6.68193'] |
| 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 | O1O2O3O4U3O5U2U1U5O6U4U6 |
| R3 orbit | {'O1O2O3O4U3O5U2U1U5O6U4U6'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U5U1O5U6U4U3O6U2 |
| Gauss code of K* | O1O2O3U4O5O4U2U1U6U5O6U3 |
| Gauss code of -K* | O1O2O3U1O4U5U4U3U2O6O5U6 |
| 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 -1 2 2 1],[ 2 0 0 0 4 2 1],[ 2 0 0 0 3 1 1],[ 1 0 0 0 1 0 1],[-2 -4 -3 -1 0 0 1],[-2 -2 -1 0 0 0 0],[-1 -1 -1 -1 -1 0 0]] |
| Primitive based matrix | [[ 0 2 2 1 -1 -2 -2],[-2 0 0 1 -1 -3 -4],[-2 0 0 0 0 -1 -2],[-1 -1 0 0 -1 -1 -1],[ 1 1 0 1 0 0 0],[ 2 3 1 1 0 0 0],[ 2 4 2 1 0 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-2,-1,1,2,2,0,-1,1,3,4,0,0,1,2,1,1,1,0,0,0] |
| Phi over symmetry | [-2,-2,-1,1,2,2,0,-1,1,3,4,0,0,1,2,1,1,1,0,0,0] |
| Phi of -K | [-2,-2,-1,1,2,2,0,1,2,0,2,1,2,1,3,1,2,3,2,1,0] |
| Phi of K* | [-2,-2,-1,1,2,2,0,1,3,2,3,2,2,0,1,1,2,2,1,1,0] |
| Phi of -K* | [-2,-2,-1,1,2,2,0,0,1,1,3,0,1,2,4,1,0,1,0,-1,0] |
| Symmetry type of based matrix | c |
| u-polynomial | 0 |
| Normalized Jones-Krushkal polynomial | 9z^2+30z+25 |
| Enhanced Jones-Krushkal polynomial | 9w^3z^2+30w^2z+25w |
| Inner characteristic polynomial | t^6+35t^4+34t^2+1 |
| Outer characteristic polynomial | t^7+53t^5+104t^3+11t |
| Flat arrow polynomial | 4*K1**3 - 4*K1*K2 - K1 + K3 + 1 |
| 2-strand cable arrow polynomial | 1504*K1**4*K2 - 2656*K1**4 + 928*K1**3*K2*K3 - 832*K1**3*K3 - 128*K1**2*K2**4 + 544*K1**2*K2**3 + 128*K1**2*K2**2*K4 - 6160*K1**2*K2**2 - 352*K1**2*K2*K4 + 6320*K1**2*K2 - 928*K1**2*K3**2 - 32*K1**2*K4**2 - 2912*K1**2 + 416*K1*K2**3*K3 - 1056*K1*K2**2*K3 - 160*K1*K2**2*K5 - 32*K1*K2*K3*K4 + 6312*K1*K2*K3 + 792*K1*K3*K4 + 32*K1*K4*K5 - 32*K2**6 + 64*K2**4*K4 - 800*K2**4 - 32*K2**3*K6 - 272*K2**2*K3**2 - 16*K2**2*K4**2 + 720*K2**2*K4 - 2446*K2**2 + 104*K2*K3*K5 + 16*K2*K4*K6 - 1556*K3**2 - 172*K4**2 - 4*K5**2 - 2*K6**2 + 2698 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{2, 6}, {3, 5}, {1, 4}], [{3, 6}, {1, 5}, {2, 4}], [{3, 6}, {2, 5}, {1, 4}], [{5, 6}, {1, 4}, {2, 3}]] |
| If K is slice | False |