| Min(phi) over symmetries of the knot is: [-2,-1,0,1,1,1,0,1,1,1,2,1,0,1,1,0,1,1,0,-1,-1] |
| Flat knots (up to 7 crossings) with same phi are :['6.1707'] |
| 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+28t^5+34t^3+5t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1707'] |
| 2-strand cable arrow polynomial of the knot is: -448*K1**4*K2**2 + 2080*K1**4*K2 - 5120*K1**4 + 1216*K1**3*K2*K3 - 1120*K1**3*K3 + 672*K1**2*K2**3 - 7184*K1**2*K2**2 - 864*K1**2*K2*K4 + 10632*K1**2*K2 - 512*K1**2*K3**2 - 4448*K1**2 + 352*K1*K2**3*K3 - 704*K1*K2**2*K3 - 160*K1*K2**2*K5 - 128*K1*K2*K3*K4 + 6536*K1*K2*K3 + 680*K1*K3*K4 + 40*K1*K4*K5 - 488*K2**4 - 272*K2**2*K3**2 - 48*K2**2*K4**2 + 728*K2**2*K4 - 3948*K2**2 + 224*K2*K3*K5 + 32*K2*K4*K6 - 1436*K3**2 - 254*K4**2 - 36*K5**2 - 4*K6**2 + 3980 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1707'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.4428', 'vk6.4523', 'vk6.5814', 'vk6.5941', 'vk6.7871', 'vk6.7978', 'vk6.9293', 'vk6.9412', 'vk6.10162', 'vk6.10235', 'vk6.10376', 'vk6.17870', 'vk6.17935', 'vk6.18276', 'vk6.18611', 'vk6.24373', 'vk6.25166', 'vk6.30053', 'vk6.30116', 'vk6.36894', 'vk6.37352', 'vk6.43808', 'vk6.44115', 'vk6.44438', 'vk6.48631', 'vk6.50530', 'vk6.50615', 'vk6.51139', 'vk6.51679', 'vk6.55839', 'vk6.56067', 'vk6.65507'] |
| 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 | O1O2O3U1U4O5O4U2U5O6U3U6 |
| R3 orbit | {'O1O2O3U1U4O5O4U2U5O6U3U6'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U4U1O4U5U2O6O5U6U3 |
| Gauss code of K* | O1O2U3O4O3U5U1U4O5O6U2U6 |
| Gauss code of -K* | O1O2U1O3O4U5U3O5O6U2U4U6 |
| 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 -1 1 1 0 1],[ 2 0 1 2 2 1 1],[ 1 -1 0 2 1 0 1],[-1 -2 -2 0 0 -1 1],[-1 -2 -1 0 0 0 1],[ 0 -1 0 1 0 0 0],[-1 -1 -1 -1 -1 0 0]] |
| Primitive based matrix | [[ 0 1 1 1 0 -1 -2],[-1 0 1 0 0 -1 -2],[-1 -1 0 -1 0 -1 -1],[-1 0 1 0 -1 -2 -2],[ 0 0 0 1 0 0 -1],[ 1 1 1 2 0 0 -1],[ 2 2 1 2 1 1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-1,-1,-1,0,1,2,-1,0,0,1,2,1,0,1,1,1,2,2,0,1,1] |
| Phi over symmetry | [-2,-1,0,1,1,1,0,1,1,1,2,1,0,1,1,0,1,1,0,-1,-1] |
| Phi of -K | [-2,-1,0,1,1,1,0,1,1,1,2,1,0,1,1,0,1,1,0,-1,-1] |
| Phi of K* | [-1,-1,-1,0,1,2,-1,-1,1,1,2,0,0,0,1,1,1,1,1,1,0] |
| Phi of -K* | [-2,-1,0,1,1,1,1,1,1,2,2,0,1,1,2,0,0,1,-1,-1,0] |
| Symmetry type of based matrix | c |
| u-polynomial | t^2-2t |
| Normalized Jones-Krushkal polynomial | 3z^2+24z+37 |
| Enhanced Jones-Krushkal polynomial | 3w^3z^2+24w^2z+37w |
| Inner characteristic polynomial | t^6+20t^4+21t^2+1 |
| Outer characteristic polynomial | t^7+28t^5+34t^3+5t |
| Flat arrow polynomial | -10*K1**2 - 4*K1*K2 + 2*K1 + 5*K2 + 2*K3 + 6 |
| 2-strand cable arrow polynomial | -448*K1**4*K2**2 + 2080*K1**4*K2 - 5120*K1**4 + 1216*K1**3*K2*K3 - 1120*K1**3*K3 + 672*K1**2*K2**3 - 7184*K1**2*K2**2 - 864*K1**2*K2*K4 + 10632*K1**2*K2 - 512*K1**2*K3**2 - 4448*K1**2 + 352*K1*K2**3*K3 - 704*K1*K2**2*K3 - 160*K1*K2**2*K5 - 128*K1*K2*K3*K4 + 6536*K1*K2*K3 + 680*K1*K3*K4 + 40*K1*K4*K5 - 488*K2**4 - 272*K2**2*K3**2 - 48*K2**2*K4**2 + 728*K2**2*K4 - 3948*K2**2 + 224*K2*K3*K5 + 32*K2*K4*K6 - 1436*K3**2 - 254*K4**2 - 36*K5**2 - 4*K6**2 + 3980 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {2, 5}, {3, 4}], [{4, 6}, {2, 5}, {1, 3}], [{4, 6}, {5}, {1, 3}, {2}]] |
| If K is slice | False |