| Min(phi) over symmetries of the knot is: [-3,-2,-1,1,2,3,0,0,3,2,4,0,2,1,3,1,0,1,1,2,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.235'] |
| Arrow polynomial of the knot is: -8*K1**2 - 4*K1*K2 + 2*K1 + 4*K2 + 2*K3 + 5 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.235', '6.379', '6.411', '6.547', '6.811', '6.818', '6.823', '6.897', '6.898', '6.1008', '6.1053', '6.1109', '6.1110', '6.1130', '6.1222', '6.1239', '6.1303', '6.1307', '6.1342', '6.1491', '6.1495', '6.1496', '6.1519', '6.1592', '6.1593', '6.1642', '6.1652', '6.1653', '6.1671', '6.1673', '6.1717'] |
| Outer characteristic polynomial of the knot is: t^7+78t^5+52t^3+4t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.235'] |
| 2-strand cable arrow polynomial of the knot is: -64*K1**6 - 64*K1**4*K2**2 + 448*K1**4*K2 - 2000*K1**4 + 160*K1**3*K2*K3 - 384*K1**3*K3 - 2112*K1**2*K2**2 - 192*K1**2*K2*K4 + 4048*K1**2*K2 - 592*K1**2*K3**2 - 32*K1**2*K3*K5 - 48*K1**2*K4**2 - 1980*K1**2 - 160*K1*K2**2*K3 - 32*K1*K2**2*K5 - 32*K1*K2*K3*K4 + 3160*K1*K2*K3 + 776*K1*K3*K4 + 120*K1*K4*K5 + 16*K1*K5*K6 - 288*K2**4 - 160*K2**2*K3**2 - 16*K2**2*K4**2 + 456*K2**2*K4 - 1820*K2**2 + 184*K2*K3*K5 + 16*K2*K4*K6 - 976*K3**2 - 328*K4**2 - 84*K5**2 - 12*K6**2 + 1990 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.235'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.11258', 'vk6.11336', 'vk6.12519', 'vk6.12630', 'vk6.13893', 'vk6.13990', 'vk6.14146', 'vk6.14371', 'vk6.14964', 'vk6.15087', 'vk6.15598', 'vk6.16070', 'vk6.17416', 'vk6.22593', 'vk6.22624', 'vk6.23924', 'vk6.24065', 'vk6.24157', 'vk6.26143', 'vk6.26560', 'vk6.30932', 'vk6.31055', 'vk6.33704', 'vk6.33781', 'vk6.34579', 'vk6.36220', 'vk6.37664', 'vk6.37713', 'vk6.42269', 'vk6.44796', 'vk6.52008', 'vk6.52102', 'vk6.54103', 'vk6.54408', 'vk6.54581', 'vk6.56496', 'vk6.56667', 'vk6.59051', 'vk6.60066', 'vk6.64559'] |
| 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 | O1O2O3O4O5U3O6U2U6U5U1U4 |
| R3 orbit | {'O1O2O3O4O5U3O6U2U6U5U1U4', 'O1O2O3O4U2O5U1U5U6U3O6U4'} |
| R3 orbit length | 2 |
| Gauss code of -K | O1O2O3O4O5U2U5U1U6U4O6U3 |
| Gauss code of K* | O1O2O3O4O5U4U1U6U5U3O6U2 |
| Gauss code of -K* | O1O2O3O4O5U4O6U3U1U6U5U2 |
| 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 -1 -3 -2 3 2 1],[ 1 0 -2 -1 3 2 1],[ 3 2 0 0 4 3 1],[ 2 1 0 0 2 1 0],[-3 -3 -4 -2 0 0 0],[-2 -2 -3 -1 0 0 0],[-1 -1 -1 0 0 0 0]] |
| Primitive based matrix | [[ 0 3 2 1 -1 -2 -3],[-3 0 0 0 -3 -2 -4],[-2 0 0 0 -2 -1 -3],[-1 0 0 0 -1 0 -1],[ 1 3 2 1 0 -1 -2],[ 2 2 1 0 1 0 0],[ 3 4 3 1 2 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-3,-2,-1,1,2,3,0,0,3,2,4,0,2,1,3,1,0,1,1,2,0] |
| Phi over symmetry | [-3,-2,-1,1,2,3,0,0,3,2,4,0,2,1,3,1,0,1,1,2,0] |
| Phi of -K | [-3,-2,-1,1,2,3,1,0,3,2,2,0,3,3,3,1,1,1,1,2,1] |
| Phi of K* | [-3,-2,-1,1,2,3,1,2,1,3,2,1,1,3,2,1,3,3,0,0,1] |
| Phi of -K* | [-3,-2,-1,1,2,3,0,2,1,3,4,1,0,1,2,1,2,3,0,0,0] |
| Symmetry type of based matrix | c |
| u-polynomial | 0 |
| Normalized Jones-Krushkal polynomial | z^2+14z+25 |
| Enhanced Jones-Krushkal polynomial | w^3z^2+14w^2z+25w |
| Inner characteristic polynomial | t^6+50t^4+20t^2+1 |
| Outer characteristic polynomial | t^7+78t^5+52t^3+4t |
| Flat arrow polynomial | -8*K1**2 - 4*K1*K2 + 2*K1 + 4*K2 + 2*K3 + 5 |
| 2-strand cable arrow polynomial | -64*K1**6 - 64*K1**4*K2**2 + 448*K1**4*K2 - 2000*K1**4 + 160*K1**3*K2*K3 - 384*K1**3*K3 - 2112*K1**2*K2**2 - 192*K1**2*K2*K4 + 4048*K1**2*K2 - 592*K1**2*K3**2 - 32*K1**2*K3*K5 - 48*K1**2*K4**2 - 1980*K1**2 - 160*K1*K2**2*K3 - 32*K1*K2**2*K5 - 32*K1*K2*K3*K4 + 3160*K1*K2*K3 + 776*K1*K3*K4 + 120*K1*K4*K5 + 16*K1*K5*K6 - 288*K2**4 - 160*K2**2*K3**2 - 16*K2**2*K4**2 + 456*K2**2*K4 - 1820*K2**2 + 184*K2*K3*K5 + 16*K2*K4*K6 - 976*K3**2 - 328*K4**2 - 84*K5**2 - 12*K6**2 + 1990 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {3, 5}, {2, 4}]] |
| If K is slice | False |