| Min(phi) over symmetries of the knot is: [-2,-1,0,0,1,2,-1,1,2,2,2,2,0,1,2,1,1,1,1,1,1] |
| Flat knots (up to 7 crossings) with same phi are :['6.1594'] |
| Arrow polynomial of the knot is: 4*K1**3 - 4*K1**2 - 4*K1*K2 - K1 + 2*K2 + K3 + 3 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.209', '6.231', '6.391', '6.419', '6.600', '6.661', '6.744', '6.812', '6.826', '6.1114', '6.1125', '6.1202', '6.1275', '6.1292', '6.1305', '6.1322', '6.1365', '6.1481', '6.1483', '6.1497', '6.1543', '6.1549', '6.1572', '6.1577', '6.1580', '6.1594', '6.1641', '6.1658', '6.1683', '6.1753', '6.1830', '6.1907', '6.1928'] |
| Outer characteristic polynomial of the knot is: t^7+39t^5+160t^3+16t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1594'] |
| 2-strand cable arrow polynomial of the knot is: -384*K1**4*K2**2 + 608*K1**4*K2 - 720*K1**4 + 224*K1**3*K2*K3 - 96*K1**3*K3 + 2048*K1**2*K2**3 - 5872*K1**2*K2**2 - 800*K1**2*K2*K4 + 5216*K1**2*K2 - 80*K1**2*K3**2 - 3620*K1**2 + 672*K1*K2**3*K3 + 224*K1*K2**2*K3*K4 - 800*K1*K2**2*K3 - 160*K1*K2**2*K5 - 96*K1*K2*K3*K4 + 4632*K1*K2*K3 - 96*K1*K2*K4*K5 + 616*K1*K3*K4 + 8*K1*K4*K5 + 8*K1*K5*K6 - 288*K2**6 + 544*K2**4*K4 - 2688*K2**4 - 160*K2**3*K6 - 704*K2**2*K3**2 - 336*K2**2*K4**2 + 2072*K2**2*K4 - 1542*K2**2 - 96*K2*K3**2*K4 + 336*K2*K3*K5 + 200*K2*K4*K6 - 1044*K3**2 - 520*K4**2 - 24*K5**2 - 10*K6**2 + 2726 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1594'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.11457', 'vk6.11758', 'vk6.12776', 'vk6.13114', 'vk6.20669', 'vk6.22108', 'vk6.28168', 'vk6.29592', 'vk6.31213', 'vk6.31560', 'vk6.32389', 'vk6.32794', 'vk6.39615', 'vk6.41856', 'vk6.46227', 'vk6.47834', 'vk6.52219', 'vk6.52502', 'vk6.53060', 'vk6.53376', 'vk6.57601', 'vk6.58763', 'vk6.62257', 'vk6.63203', 'vk6.63784', 'vk6.63900', 'vk6.64217', 'vk6.64398', 'vk6.67061', 'vk6.67928', 'vk6.69680', 'vk6.70362'] |
| 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 | O1O2O3U4O5U6U3O6O4U1U2U5 |
| R3 orbit | {'O1O2O3U4O5U6U3O6O4U1U2U5'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U4U2U3O5O6U1U6O4U5 |
| Gauss code of K* | O1O2O3U1U2U4O5U3O6O4U6U5 |
| Gauss code of -K* | O1O2O3U4U5O6O5U1O4U6U2U3 |
| 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 0 1 0 2 -1],[ 2 0 1 2 1 2 1],[ 0 -1 0 2 -1 1 -1],[-1 -2 -2 0 0 -1 -1],[ 0 -1 1 0 0 2 -1],[-2 -2 -1 1 -2 0 -2],[ 1 -1 1 1 1 2 0]] |
| Primitive based matrix | [[ 0 2 1 0 0 -1 -2],[-2 0 1 -1 -2 -2 -2],[-1 -1 0 -2 0 -1 -2],[ 0 1 2 0 -1 -1 -1],[ 0 2 0 1 0 -1 -1],[ 1 2 1 1 1 0 -1],[ 2 2 2 1 1 1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,0,0,1,2,-1,1,2,2,2,2,0,1,2,1,1,1,1,1,1] |
| Phi over symmetry | [-2,-1,0,0,1,2,-1,1,2,2,2,2,0,1,2,1,1,1,1,1,1] |
| Phi of -K | [-2,-1,0,0,1,2,0,1,1,1,2,0,0,1,1,-1,1,0,-1,1,2] |
| Phi of K* | [-2,-1,0,0,1,2,2,0,1,1,2,1,-1,1,1,1,0,1,0,1,0] |
| Phi of -K* | [-2,-1,0,0,1,2,1,1,1,2,2,1,1,1,2,-1,2,1,0,2,-1] |
| Symmetry type of based matrix | c |
| u-polynomial | 0 |
| Normalized Jones-Krushkal polynomial | 5z^2+22z+25 |
| Enhanced Jones-Krushkal polynomial | -2w^4z^2+7w^3z^2-4w^3z+26w^2z+25w |
| Inner characteristic polynomial | t^6+29t^4+100t^2+4 |
| Outer characteristic polynomial | t^7+39t^5+160t^3+16t |
| Flat arrow polynomial | 4*K1**3 - 4*K1**2 - 4*K1*K2 - K1 + 2*K2 + K3 + 3 |
| 2-strand cable arrow polynomial | -384*K1**4*K2**2 + 608*K1**4*K2 - 720*K1**4 + 224*K1**3*K2*K3 - 96*K1**3*K3 + 2048*K1**2*K2**3 - 5872*K1**2*K2**2 - 800*K1**2*K2*K4 + 5216*K1**2*K2 - 80*K1**2*K3**2 - 3620*K1**2 + 672*K1*K2**3*K3 + 224*K1*K2**2*K3*K4 - 800*K1*K2**2*K3 - 160*K1*K2**2*K5 - 96*K1*K2*K3*K4 + 4632*K1*K2*K3 - 96*K1*K2*K4*K5 + 616*K1*K3*K4 + 8*K1*K4*K5 + 8*K1*K5*K6 - 288*K2**6 + 544*K2**4*K4 - 2688*K2**4 - 160*K2**3*K6 - 704*K2**2*K3**2 - 336*K2**2*K4**2 + 2072*K2**2*K4 - 1542*K2**2 - 96*K2*K3**2*K4 + 336*K2*K3*K5 + 200*K2*K4*K6 - 1044*K3**2 - 520*K4**2 - 24*K5**2 - 10*K6**2 + 2726 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{2, 6}, {3, 5}, {1, 4}], [{3, 6}, {1, 5}, {2, 4}], [{6}, {3, 5}, {1, 4}, {2}]] |
| If K is slice | False |