| Min(phi) over symmetries of the knot is: [-3,-2,0,1,2,2,0,3,1,2,3,2,0,1,2,1,1,1,0,0,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.468'] |
| Arrow polynomial of the knot is: 4*K1**3 - 2*K1**2 - 2*K1*K2 - 2*K1 + K2 + 2 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['4.2', '6.303', '6.338', '6.381', '6.432', '6.468', '6.558', '6.583', '6.597', '6.607', '6.634', '6.637', '6.643', '6.654', '6.667', '6.701', '6.709', '6.712', '6.718', '6.728', '6.767', '6.801', '6.825', '6.827', '6.974', '6.994', '6.1042', '6.1061', '6.1069', '6.1181', '6.1271', '6.1286', '6.1287', '6.1289', '6.1297', '6.1337', '6.1355'] |
| Outer characteristic polynomial of the knot is: t^7+71t^5+91t^3+12t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.468'] |
| 2-strand cable arrow polynomial of the knot is: -64*K1**4 + 96*K1**3*K2*K3 - 64*K1**3*K3 - 576*K1**2*K2**4 + 896*K1**2*K2**3 + 160*K1**2*K2**2*K4 - 5776*K1**2*K2**2 - 576*K1**2*K2*K4 + 5880*K1**2*K2 - 64*K1**2*K3**2 - 192*K1**2*K4**2 - 4760*K1**2 + 992*K1*K2**3*K3 - 1056*K1*K2**2*K3 - 512*K1*K2**2*K5 - 384*K1*K2*K3*K4 - 64*K1*K2*K3*K6 + 6512*K1*K2*K3 - 64*K1*K2*K4*K5 + 1152*K1*K3*K4 + 472*K1*K4*K5 + 48*K1*K5*K6 - 32*K2**6 + 32*K2**4*K4 - 1272*K2**4 - 560*K2**2*K3**2 - 72*K2**2*K4**2 + 1888*K2**2*K4 - 3456*K2**2 + 808*K2*K3*K5 + 112*K2*K4*K6 + 16*K3**2*K6 - 1992*K3**2 - 902*K4**2 - 328*K5**2 - 40*K6**2 + 3740 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.468'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.4735', 'vk6.5059', 'vk6.6269', 'vk6.6712', 'vk6.8236', 'vk6.8683', 'vk6.9627', 'vk6.9945', 'vk6.20645', 'vk6.22078', 'vk6.28135', 'vk6.29566', 'vk6.39569', 'vk6.41802', 'vk6.46188', 'vk6.47808', 'vk6.48775', 'vk6.48985', 'vk6.49585', 'vk6.49790', 'vk6.50789', 'vk6.51004', 'vk6.51279', 'vk6.51475', 'vk6.57561', 'vk6.58733', 'vk6.62239', 'vk6.63187', 'vk6.67039', 'vk6.67914', 'vk6.69668', 'vk6.70351'] |
| 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 | O1O2O3O4O5U6U4O6U2U1U5U3 |
| R3 orbit | {'O1O2O3O4O5U6U4O6U2U1U5U3'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4O5U3U1U5U4O6U2U6 |
| Gauss code of K* | O1O2O3O4U2U1U4U5U3O6O5U6 |
| Gauss code of -K* | O1O2O3O4U5O6O5U2U6U1U4U3 |
| 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 2 0 3 -1],[ 2 0 0 3 1 3 1],[ 2 0 0 2 1 2 1],[-2 -3 -2 0 0 1 -3],[ 0 -1 -1 0 0 0 0],[-3 -3 -2 -1 0 0 -3],[ 1 -1 -1 3 0 3 0]] |
| Primitive based matrix | [[ 0 3 2 0 -1 -2 -2],[-3 0 -1 0 -3 -2 -3],[-2 1 0 0 -3 -2 -3],[ 0 0 0 0 0 -1 -1],[ 1 3 3 0 0 -1 -1],[ 2 2 2 1 1 0 0],[ 2 3 3 1 1 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-3,-2,0,1,2,2,1,0,3,2,3,0,3,2,3,0,1,1,1,1,0] |
| Phi over symmetry | [-3,-2,0,1,2,2,0,3,1,2,3,2,0,1,2,1,1,1,0,0,0] |
| Phi of -K | [-2,-2,-1,0,2,3,0,0,1,1,2,0,1,2,3,1,0,1,2,3,0] |
| Phi of K* | [-3,-2,0,1,2,2,0,3,1,2,3,2,0,1,2,1,1,1,0,0,0] |
| Phi of -K* | [-2,-2,-1,0,2,3,0,1,1,2,2,1,1,3,3,0,3,3,0,0,1] |
| Symmetry type of based matrix | c |
| u-polynomial | -t^3+t^2+t |
| Normalized Jones-Krushkal polynomial | 7z^2+24z+21 |
| Enhanced Jones-Krushkal polynomial | 7w^3z^2-4w^3z+28w^2z+21w |
| Inner characteristic polynomial | t^6+49t^4+44t^2 |
| Outer characteristic polynomial | t^7+71t^5+91t^3+12t |
| Flat arrow polynomial | 4*K1**3 - 2*K1**2 - 2*K1*K2 - 2*K1 + K2 + 2 |
| 2-strand cable arrow polynomial | -64*K1**4 + 96*K1**3*K2*K3 - 64*K1**3*K3 - 576*K1**2*K2**4 + 896*K1**2*K2**3 + 160*K1**2*K2**2*K4 - 5776*K1**2*K2**2 - 576*K1**2*K2*K4 + 5880*K1**2*K2 - 64*K1**2*K3**2 - 192*K1**2*K4**2 - 4760*K1**2 + 992*K1*K2**3*K3 - 1056*K1*K2**2*K3 - 512*K1*K2**2*K5 - 384*K1*K2*K3*K4 - 64*K1*K2*K3*K6 + 6512*K1*K2*K3 - 64*K1*K2*K4*K5 + 1152*K1*K3*K4 + 472*K1*K4*K5 + 48*K1*K5*K6 - 32*K2**6 + 32*K2**4*K4 - 1272*K2**4 - 560*K2**2*K3**2 - 72*K2**2*K4**2 + 1888*K2**2*K4 - 3456*K2**2 + 808*K2*K3*K5 + 112*K2*K4*K6 + 16*K3**2*K6 - 1992*K3**2 - 902*K4**2 - 328*K5**2 - 40*K6**2 + 3740 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{3, 6}, {2, 5}, {1, 4}]] |
| If K is slice | False |