| Min(phi) over symmetries of the knot is: [-3,-2,0,1,1,3,0,3,1,1,4,1,0,1,2,0,1,2,0,0,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.655'] |
| Arrow polynomial of the knot is: -10*K1**2 - 4*K1*K2 + 2*K1 + 5*K2 + 2*K3 + 6 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.425', '6.655', '6.755', '6.769', '6.792', '6.1240', '6.1494', '6.1522', '6.1534', '6.1587', '6.1707', '6.1746', '6.1747', '6.1786', '6.1814', '6.1828', '6.1835', '6.1854', '6.1870'] |
| Outer characteristic polynomial of the knot is: t^7+62t^5+80t^3+4t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.655'] |
| 2-strand cable arrow polynomial of the knot is: -64*K1**6 - 64*K1**4*K2**2 + 576*K1**4*K2 - 2384*K1**4 + 160*K1**3*K2*K3 - 384*K1**3*K3 + 352*K1**2*K2**3 - 4048*K1**2*K2**2 + 128*K1**2*K2*K3**2 - 192*K1**2*K2*K4 + 6032*K1**2*K2 - 848*K1**2*K3**2 - 48*K1**2*K4**2 - 3144*K1**2 - 416*K1*K2**2*K3 - 32*K1*K2**2*K5 - 256*K1*K2*K3*K4 + 4920*K1*K2*K3 + 1048*K1*K3*K4 + 104*K1*K4*K5 + 16*K1*K5*K6 - 712*K2**4 - 288*K2**2*K3**2 - 16*K2**2*K4**2 + 952*K2**2*K4 - 2756*K2**2 + 408*K2*K3*K5 + 16*K2*K4*K6 - 1452*K3**2 - 506*K4**2 - 124*K5**2 - 12*K6**2 + 3032 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.655'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.13885', 'vk6.13982', 'vk6.14119', 'vk6.14340', 'vk6.14956', 'vk6.15079', 'vk6.15573', 'vk6.16043', 'vk6.16299', 'vk6.16324', 'vk6.17417', 'vk6.22614', 'vk6.22647', 'vk6.23925', 'vk6.33696', 'vk6.33773', 'vk6.34132', 'vk6.34256', 'vk6.34598', 'vk6.36196', 'vk6.36221', 'vk6.42298', 'vk6.53871', 'vk6.53914', 'vk6.54094', 'vk6.54416', 'vk6.54582', 'vk6.55575', 'vk6.59029', 'vk6.59058', 'vk6.60067', 'vk6.64554'] |
| 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 | O1O2O3O4U2O5U1U5O6U3U6U4 |
| R3 orbit | {'O1O2O3O4U2O5U1U5O6U3U6U4'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U1U5U2O5U6U4O6U3 |
| Gauss code of K* | O1O2O3U4U5U1U3O5U6O4O6U2 |
| Gauss code of -K* | O1O2O3U2O4O5U4O6U1U3U6U5 |
| 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 0 3 1 1],[ 3 0 0 3 4 1 1],[ 2 0 0 1 2 0 1],[ 0 -3 -1 0 2 0 1],[-3 -4 -2 -2 0 0 0],[-1 -1 0 0 0 0 0],[-1 -1 -1 -1 0 0 0]] |
| Primitive based matrix | [[ 0 3 1 1 0 -2 -3],[-3 0 0 0 -2 -2 -4],[-1 0 0 0 0 0 -1],[-1 0 0 0 -1 -1 -1],[ 0 2 0 1 0 -1 -3],[ 2 2 0 1 1 0 0],[ 3 4 1 1 3 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-3,-1,-1,0,2,3,0,0,2,2,4,0,0,0,1,1,1,1,1,3,0] |
| Phi over symmetry | [-3,-2,0,1,1,3,0,3,1,1,4,1,0,1,2,0,1,2,0,0,0] |
| Phi of -K | [-3,-2,0,1,1,3,1,0,3,3,2,1,2,3,3,0,1,1,0,2,2] |
| Phi of K* | [-3,-1,-1,0,2,3,2,2,1,3,2,0,0,2,3,1,3,3,1,0,1] |
| Phi of -K* | [-3,-2,0,1,1,3,0,3,1,1,4,1,0,1,2,0,1,2,0,0,0] |
| Symmetry type of based matrix | c |
| u-polynomial | t^2-2t |
| Normalized Jones-Krushkal polynomial | 3z^2+20z+29 |
| Enhanced Jones-Krushkal polynomial | 3w^3z^2+20w^2z+29w |
| Inner characteristic polynomial | t^6+38t^4+27t^2 |
| Outer characteristic polynomial | t^7+62t^5+80t^3+4t |
| Flat arrow polynomial | -10*K1**2 - 4*K1*K2 + 2*K1 + 5*K2 + 2*K3 + 6 |
| 2-strand cable arrow polynomial | -64*K1**6 - 64*K1**4*K2**2 + 576*K1**4*K2 - 2384*K1**4 + 160*K1**3*K2*K3 - 384*K1**3*K3 + 352*K1**2*K2**3 - 4048*K1**2*K2**2 + 128*K1**2*K2*K3**2 - 192*K1**2*K2*K4 + 6032*K1**2*K2 - 848*K1**2*K3**2 - 48*K1**2*K4**2 - 3144*K1**2 - 416*K1*K2**2*K3 - 32*K1*K2**2*K5 - 256*K1*K2*K3*K4 + 4920*K1*K2*K3 + 1048*K1*K3*K4 + 104*K1*K4*K5 + 16*K1*K5*K6 - 712*K2**4 - 288*K2**2*K3**2 - 16*K2**2*K4**2 + 952*K2**2*K4 - 2756*K2**2 + 408*K2*K3*K5 + 16*K2*K4*K6 - 1452*K3**2 - 506*K4**2 - 124*K5**2 - 12*K6**2 + 3032 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {2, 5}, {3, 4}], [{3, 6}, {1, 5}, {2, 4}]] |
| If K is slice | False |