| Min(phi) over symmetries of the knot is: [-2,-1,0,1,1,1,0,1,1,2,3,0,1,2,1,0,0,1,0,-1,-1] |
| Flat knots (up to 7 crossings) with same phi are :['6.1832'] |
| Arrow polynomial of the knot is: 4*K1**3 - 10*K1**2 - 4*K1*K2 - K1 + 5*K2 + K3 + 6 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.241', '6.341', '6.542', '6.567', '6.699', '6.713', '6.771', '6.791', '6.1025', '6.1039', '6.1041', '6.1072', '6.1077', '6.1121', '6.1123', '6.1499', '6.1502', '6.1531', '6.1645', '6.1648', '6.1726', '6.1727', '6.1761', '6.1784', '6.1807', '6.1823', '6.1832', '6.1869', '6.1873', '6.1874'] |
| Outer characteristic polynomial of the knot is: t^7+22t^5+46t^3+5t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1719', '6.1832', '7.40949'] |
| 2-strand cable arrow polynomial of the knot is: -64*K1**6 - 320*K1**4*K2**2 + 3552*K1**4*K2 - 7472*K1**4 - 128*K1**3*K2**2*K3 + 672*K1**3*K2*K3 + 32*K1**3*K3*K4 - 2080*K1**3*K3 + 992*K1**2*K2**3 - 6400*K1**2*K2**2 + 128*K1**2*K2*K3**2 - 256*K1**2*K2*K4 + 12320*K1**2*K2 - 816*K1**2*K3**2 - 32*K1**2*K3*K5 - 16*K1**2*K4**2 - 4860*K1**2 + 256*K1*K2**3*K3 - 1024*K1*K2**2*K3 - 96*K1*K2**2*K5 - 64*K1*K2*K3*K4 + 6416*K1*K2*K3 + 936*K1*K3*K4 + 40*K1*K4*K5 - 32*K2**6 + 64*K2**4*K4 - 808*K2**4 - 32*K2**3*K6 - 224*K2**2*K3**2 - 16*K2**2*K4**2 + 736*K2**2*K4 - 4246*K2**2 + 128*K2*K3*K5 + 16*K2*K4*K6 - 1600*K3**2 - 302*K4**2 - 20*K5**2 - 2*K6**2 + 4620 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1832'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.4082', 'vk6.4113', 'vk6.5320', 'vk6.5351', 'vk6.7450', 'vk6.7481', 'vk6.8951', 'vk6.8982', 'vk6.10104', 'vk6.10275', 'vk6.10298', 'vk6.14544', 'vk6.15291', 'vk6.15418', 'vk6.15768', 'vk6.16183', 'vk6.29854', 'vk6.29885', 'vk6.33933', 'vk6.34010', 'vk6.34211', 'vk6.34394', 'vk6.48464', 'vk6.49165', 'vk6.50218', 'vk6.50247', 'vk6.51580', 'vk6.53968', 'vk6.54031', 'vk6.54172', 'vk6.54473', 'vk6.63301'] |
| 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 | O1O2O3U1U4O5U3O4O6U5U6U2 |
| R3 orbit | {'O1O2O3U1U4O5U3O4O6U5U6U2'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U2U4U5O4O6U1O5U6U3 |
| Gauss code of K* | O1O2O3U4U3U5O4O6U1O5U6U2 |
| Gauss code of -K* | O1O2O3U2U4O5U3O4O6U5U1U6 |
| 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 0 -1 1],[ 2 0 2 1 1 1 0],[-1 -2 0 0 -1 -1 1],[-1 -1 0 0 -1 0 1],[ 0 -1 1 1 0 -1 0],[ 1 -1 1 0 1 0 1],[-1 0 -1 -1 0 -1 0]] |
| Primitive based matrix | [[ 0 1 1 1 0 -1 -2],[-1 0 1 0 -1 0 -1],[-1 -1 0 -1 0 -1 0],[-1 0 1 0 -1 -1 -2],[ 0 1 0 1 0 -1 -1],[ 1 0 1 1 1 0 -1],[ 2 1 0 2 1 1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-1,-1,-1,0,1,2,-1,0,1,0,1,1,0,1,0,1,1,2,1,1,1] |
| Phi over symmetry | [-2,-1,0,1,1,1,0,1,1,2,3,0,1,2,1,0,0,1,0,-1,-1] |
| Phi of -K | [-2,-1,0,1,1,1,0,1,1,2,3,0,1,2,1,0,0,1,0,-1,-1] |
| Phi of K* | [-1,-1,-1,0,1,2,-1,-1,1,1,3,0,0,1,1,0,2,2,0,1,0] |
| Phi of -K* | [-2,-1,0,1,1,1,1,1,0,1,2,1,1,0,1,0,1,1,-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+14t^4+25t^2+1 |
| Outer characteristic polynomial | t^7+22t^5+46t^3+5t |
| Flat arrow polynomial | 4*K1**3 - 10*K1**2 - 4*K1*K2 - K1 + 5*K2 + K3 + 6 |
| 2-strand cable arrow polynomial | -64*K1**6 - 320*K1**4*K2**2 + 3552*K1**4*K2 - 7472*K1**4 - 128*K1**3*K2**2*K3 + 672*K1**3*K2*K3 + 32*K1**3*K3*K4 - 2080*K1**3*K3 + 992*K1**2*K2**3 - 6400*K1**2*K2**2 + 128*K1**2*K2*K3**2 - 256*K1**2*K2*K4 + 12320*K1**2*K2 - 816*K1**2*K3**2 - 32*K1**2*K3*K5 - 16*K1**2*K4**2 - 4860*K1**2 + 256*K1*K2**3*K3 - 1024*K1*K2**2*K3 - 96*K1*K2**2*K5 - 64*K1*K2*K3*K4 + 6416*K1*K2*K3 + 936*K1*K3*K4 + 40*K1*K4*K5 - 32*K2**6 + 64*K2**4*K4 - 808*K2**4 - 32*K2**3*K6 - 224*K2**2*K3**2 - 16*K2**2*K4**2 + 736*K2**2*K4 - 4246*K2**2 + 128*K2*K3*K5 + 16*K2*K4*K6 - 1600*K3**2 - 302*K4**2 - 20*K5**2 - 2*K6**2 + 4620 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {4, 5}, {2, 3}], [{1, 6}, {5}, {4}, {2, 3}], [{3, 6}, {4, 5}, {1, 2}]] |
| If K is slice | False |