| Min(phi) over symmetries of the knot is: [-3,-3,-2,2,3,3,-1,0,4,3,4,0,3,1,2,3,2,3,1,1,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.201'] |
| Arrow polynomial of the knot is: -4*K1**2 - 4*K1*K2 + 2*K1 + 2*K2 + 2*K3 + 3 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.65', '6.137', '6.201', '6.203', '6.214', '6.310', '6.314', '6.332', '6.385', '6.386', '6.401', '6.516', '6.564', '6.571', '6.572', '6.578', '6.621', '6.626', '6.716', '6.773', '6.807', '6.814', '6.821', '6.940', '6.966', '6.1036', '6.1071', '6.1108', '6.1111', '6.1131', '6.1188', '6.1203', '6.1206', '6.1220', '6.1340', '6.1387', '6.1548', '6.1663', '6.1680', '6.1693', '6.1831', '6.1932'] |
| Outer characteristic polynomial of the knot is: t^7+120t^5+153t^3+4t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.201'] |
| 2-strand cable arrow polynomial of the knot is: -192*K1**3*K3 - 1248*K1**2*K2**2 + 128*K1**2*K2*K3**2 + 3256*K1**2*K2 - 384*K1**2*K3**2 - 32*K1**2*K3*K5 - 3864*K1**2 + 192*K1*K2**3*K3 - 992*K1*K2**2*K3 - 64*K1*K2**2*K5 + 32*K1*K2*K3**3 - 224*K1*K2*K3*K4 + 4472*K1*K2*K3 + 960*K1*K3*K4 + 88*K1*K4*K5 + 8*K1*K5*K6 - 368*K2**4 - 608*K2**2*K3**2 - 80*K2**2*K4**2 + 1056*K2**2*K4 - 3124*K2**2 - 64*K2*K3**2*K4 + 488*K2*K3*K5 + 96*K2*K4*K6 - 32*K3**4 + 48*K3**2*K6 - 1864*K3**2 - 580*K4**2 - 104*K5**2 - 36*K6**2 + 3034 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.201'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.73746', 'vk6.73864', 'vk6.74201', 'vk6.74821', 'vk6.75663', 'vk6.75867', 'vk6.76378', 'vk6.76878', 'vk6.78674', 'vk6.78863', 'vk6.79238', 'vk6.79717', 'vk6.80288', 'vk6.80417', 'vk6.80726', 'vk6.81077', 'vk6.81618', 'vk6.81814', 'vk6.81998', 'vk6.82317', 'vk6.82372', 'vk6.82725', 'vk6.83225', 'vk6.84230', 'vk6.84324', 'vk6.84421', 'vk6.84504', 'vk6.85659', 'vk6.86548', 'vk6.87562', 'vk6.88265', 'vk6.89415'] |
| 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 | O1O2O3O4O5U2O6U3U1U6U5U4 |
| R3 orbit | {'O1O2O3O4O5U2O6U3U1U6U5U4'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4O5U2U1U6U5U3O6U4 |
| Gauss code of K* | O1O2O3O4O5U2U6U1U5U4O6U3 |
| Gauss code of -K* | O1O2O3O4O5U3O6U2U1U5U6U4 |
| 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 -3 -2 3 3 2],[ 3 0 -1 1 5 4 2],[ 3 1 0 1 3 2 1],[ 2 -1 -1 0 3 2 1],[-3 -5 -3 -3 0 0 0],[-3 -4 -2 -2 0 0 0],[-2 -2 -1 -1 0 0 0]] |
| Primitive based matrix | [[ 0 3 3 2 -2 -3 -3],[-3 0 0 0 -2 -2 -4],[-3 0 0 0 -3 -3 -5],[-2 0 0 0 -1 -1 -2],[ 2 2 3 1 0 -1 -1],[ 3 2 3 1 1 0 1],[ 3 4 5 2 1 -1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-3,-3,-2,2,3,3,0,0,2,2,4,0,3,3,5,1,1,2,1,1,-1] |
| Phi over symmetry | [-3,-3,-2,2,3,3,-1,0,4,3,4,0,3,1,2,3,2,3,1,1,0] |
| Phi of -K | [-3,-3,-2,2,3,3,-1,0,4,3,4,0,3,1,2,3,2,3,1,1,0] |
| Phi of K* | [-3,-3,-2,2,3,3,0,1,2,1,3,1,3,2,4,3,3,4,0,0,-1] |
| Phi of -K* | [-3,-3,-2,2,3,3,-1,1,2,4,5,1,1,2,3,1,2,3,0,0,0] |
| Symmetry type of based matrix | c |
| u-polynomial | 0 |
| Normalized Jones-Krushkal polynomial | 5z^2+22z+25 |
| Enhanced Jones-Krushkal polynomial | 5w^3z^2+22w^2z+25w |
| Inner characteristic polynomial | t^6+76t^4+11t^2 |
| Outer characteristic polynomial | t^7+120t^5+153t^3+4t |
| Flat arrow polynomial | -4*K1**2 - 4*K1*K2 + 2*K1 + 2*K2 + 2*K3 + 3 |
| 2-strand cable arrow polynomial | -192*K1**3*K3 - 1248*K1**2*K2**2 + 128*K1**2*K2*K3**2 + 3256*K1**2*K2 - 384*K1**2*K3**2 - 32*K1**2*K3*K5 - 3864*K1**2 + 192*K1*K2**3*K3 - 992*K1*K2**2*K3 - 64*K1*K2**2*K5 + 32*K1*K2*K3**3 - 224*K1*K2*K3*K4 + 4472*K1*K2*K3 + 960*K1*K3*K4 + 88*K1*K4*K5 + 8*K1*K5*K6 - 368*K2**4 - 608*K2**2*K3**2 - 80*K2**2*K4**2 + 1056*K2**2*K4 - 3124*K2**2 - 64*K2*K3**2*K4 + 488*K2*K3*K5 + 96*K2*K4*K6 - 32*K3**4 + 48*K3**2*K6 - 1864*K3**2 - 580*K4**2 - 104*K5**2 - 36*K6**2 + 3034 |
| Genus of based matrix | 0 |
| Fillings of based matrix | [[{3, 6}, {2, 5}, {1, 4}]] |
| If K is slice | True |