| Min(phi) over symmetries of the knot is: [-3,-1,0,1,1,2,0,1,1,2,4,0,0,0,1,1,1,1,-1,-1,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.690'] |
| Arrow polynomial of the knot is: -10*K1**2 - 2*K1*K2 + K1 + 5*K2 + K3 + 6 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.574', '6.593', '6.604', '6.649', '6.650', '6.673', '6.690', '6.783', '6.973', '6.985', '6.1033', '6.1035'] |
| Outer characteristic polynomial of the knot is: t^7+44t^5+50t^3 |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.690'] |
| 2-strand cable arrow polynomial of the knot is: -192*K1**4*K2**2 + 672*K1**4*K2 - 1456*K1**4 + 96*K1**3*K2*K3 + 32*K1**3*K3*K4 + 128*K1**2*K2**3 - 1440*K1**2*K2**2 + 2360*K1**2*K2 - 176*K1**2*K3**2 - 32*K1**2*K4**2 - 1128*K1**2 + 1320*K1*K2*K3 + 272*K1*K3*K4 + 8*K1*K4*K5 - 104*K2**4 - 32*K2**2*K3**2 - 8*K2**2*K4**2 + 184*K2**2*K4 - 1166*K2**2 + 64*K2*K3*K5 + 8*K2*K4*K6 - 472*K3**2 - 174*K4**2 - 24*K5**2 - 2*K6**2 + 1260 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.690'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.4431', 'vk6.4528', 'vk6.4843', 'vk6.5186', 'vk6.5817', 'vk6.5946', 'vk6.6414', 'vk6.6433', 'vk6.6845', 'vk6.7991', 'vk6.8371', 'vk6.8398', 'vk6.8798', 'vk6.9304', 'vk6.9425', 'vk6.9738', 'vk6.17892', 'vk6.17957', 'vk6.18269', 'vk6.18606', 'vk6.24399', 'vk6.25157', 'vk6.30040', 'vk6.30101', 'vk6.36887', 'vk6.37347', 'vk6.39821', 'vk6.39839', 'vk6.43834', 'vk6.44104', 'vk6.44429', 'vk6.46381', 'vk6.46401', 'vk6.47958', 'vk6.47980', 'vk6.48623', 'vk6.49080', 'vk6.49918', 'vk6.50612', 'vk6.51134'] |
| 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 | O1O2O3O4U3O5U4U2O6U1U6U5 |
| R3 orbit | {'O1O2O3O4U3O5U4U2O6U1U6U5', 'O1O2O3U2O4O5U3U4O6U1U6U5'} |
| R3 orbit length | 2 |
| Gauss code of -K | O1O2O3O4U5U6U4O6U3U1O5U2 |
| Gauss code of K* | O1O2O3U1U4U5U6O5U3O6O4U2 |
| Gauss code of -K* | O1O2O3U2O4O5U1O6U5U6U4U3 |
| Diagrammatic symmetry type | c |
| Flat genus of the diagram | 2 |
| If K is checkerboard colorable | False |
| If K is almost classical | False |
| Based matrix from Gauss code | [[ 0 -2 -1 -1 0 3 1],[ 2 0 0 -1 1 4 1],[ 1 0 0 -1 1 2 0],[ 1 1 1 0 1 1 0],[ 0 -1 -1 -1 0 1 0],[-3 -4 -2 -1 -1 0 0],[-1 -1 0 0 0 0 0]] |
| Primitive based matrix | [[ 0 3 1 0 -1 -1 -2],[-3 0 0 -1 -1 -2 -4],[-1 0 0 0 0 0 -1],[ 0 1 0 0 -1 -1 -1],[ 1 1 0 1 0 1 1],[ 1 2 0 1 -1 0 0],[ 2 4 1 1 -1 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-3,-1,0,1,1,2,0,1,1,2,4,0,0,0,1,1,1,1,-1,-1,0] |
| Phi over symmetry | [-3,-1,0,1,1,2,0,1,1,2,4,0,0,0,1,1,1,1,-1,-1,0] |
| Phi of -K | [-2,-1,-1,0,1,3,1,2,1,2,1,1,0,2,2,0,2,3,1,2,2] |
| Phi of K* | [-3,-1,0,1,1,2,2,2,2,3,1,1,2,2,2,0,0,1,-1,1,2] |
| Phi of -K* | [-2,-1,-1,0,1,3,-1,0,1,1,4,1,1,0,1,1,0,2,0,1,0] |
| Symmetry type of based matrix | c |
| u-polynomial | -t^3+t^2+t |
| Normalized Jones-Krushkal polynomial | 11z+23 |
| Enhanced Jones-Krushkal polynomial | 11w^2z+23w |
| Inner characteristic polynomial | t^6+28t^4+21t^2 |
| Outer characteristic polynomial | t^7+44t^5+50t^3 |
| Flat arrow polynomial | -10*K1**2 - 2*K1*K2 + K1 + 5*K2 + K3 + 6 |
| 2-strand cable arrow polynomial | -192*K1**4*K2**2 + 672*K1**4*K2 - 1456*K1**4 + 96*K1**3*K2*K3 + 32*K1**3*K3*K4 + 128*K1**2*K2**3 - 1440*K1**2*K2**2 + 2360*K1**2*K2 - 176*K1**2*K3**2 - 32*K1**2*K4**2 - 1128*K1**2 + 1320*K1*K2*K3 + 272*K1*K3*K4 + 8*K1*K4*K5 - 104*K2**4 - 32*K2**2*K3**2 - 8*K2**2*K4**2 + 184*K2**2*K4 - 1166*K2**2 + 64*K2*K3*K5 + 8*K2*K4*K6 - 472*K3**2 - 174*K4**2 - 24*K5**2 - 2*K6**2 + 1260 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{4, 6}, {1, 5}, {2, 3}], [{4, 6}, {2, 5}, {1, 3}]] |
| If K is slice | False |