| Min(phi) over symmetries of the knot is: [-2,-1,0,0,1,2,0,0,1,2,4,2,2,1,1,1,-1,0,0,2,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.1481'] |
| 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+35t^5+110t^3+15t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1481'] |
| 2-strand cable arrow polynomial of the knot is: -128*K1**4*K2**2 + 192*K1**4*K2 - 208*K1**4 + 64*K1**3*K2*K3 - 96*K1**3*K3 - 1536*K1**2*K2**4 + 3840*K1**2*K2**3 + 64*K1**2*K2**2*K4 - 8208*K1**2*K2**2 - 96*K1**2*K2*K4 + 5920*K1**2*K2 - 16*K1**2*K3**2 - 3840*K1**2 + 2656*K1*K2**3*K3 - 2112*K1*K2**2*K3 - 384*K1*K2**2*K5 - 32*K1*K2*K3*K4 + 5816*K1*K2*K3 + 88*K1*K3*K4 - 32*K2**6 + 64*K2**4*K4 - 4192*K2**4 - 32*K2**3*K6 - 944*K2**2*K3**2 - 16*K2**2*K4**2 + 2352*K2**2*K4 - 702*K2**2 + 232*K2*K3*K5 + 16*K2*K4*K6 - 1252*K3**2 - 144*K4**2 - 20*K5**2 - 2*K6**2 + 2686 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1481'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.70459', 'vk6.70476', 'vk6.70523', 'vk6.70598', 'vk6.70629', 'vk6.70656', 'vk6.70752', 'vk6.70840', 'vk6.70914', 'vk6.70944', 'vk6.71004', 'vk6.71109', 'vk6.71153', 'vk6.71170', 'vk6.71241', 'vk6.71300', 'vk6.71310', 'vk6.71327', 'vk6.73546', 'vk6.74355', 'vk6.75004', 'vk6.75301', 'vk6.76575', 'vk6.76646', 'vk6.76979', 'vk6.78285', 'vk6.79399', 'vk6.79944', 'vk6.81506', 'vk6.86860', 'vk6.88081', 'vk6.89228'] |
| 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 | O1O2O3U1O4U2U3O5O6U4U5U6 |
| R3 orbit | {'O1O2O3U1O4U2U3O5O6U4U5U6'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U4U5U6O4O5U1U2O6U3 |
| Gauss code of K* | O1O2O3U4U5U6O4U1O5O6U2U3 |
| Gauss code of -K* | O1O2O3U1U2O4O5U3O6U4U5U6 |
| 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 0 2],[ 2 0 1 2 2 0 0],[ 1 -1 0 1 2 1 1],[-1 -2 -1 0 1 1 1],[ 0 -2 -2 -1 0 1 2],[ 0 0 -1 -1 -1 0 1],[-2 0 -1 -1 -2 -1 0]] |
| Primitive based matrix | [[ 0 2 1 0 0 -1 -2],[-2 0 -1 -1 -2 -1 0],[-1 1 0 1 1 -1 -2],[ 0 1 -1 0 -1 -1 0],[ 0 2 -1 1 0 -2 -2],[ 1 1 1 1 2 0 -1],[ 2 0 2 0 2 1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,0,0,1,2,1,1,2,1,0,-1,-1,1,2,1,1,0,2,2,1] |
| Phi over symmetry | [-2,-1,0,0,1,2,0,0,1,2,4,2,2,1,1,1,-1,0,0,2,0] |
| Phi of -K | [-2,-1,0,0,1,2,0,0,2,1,4,-1,0,1,2,-1,2,0,2,1,0] |
| Phi of K* | [-2,-1,0,0,1,2,0,0,1,2,4,2,2,1,1,1,-1,0,0,2,0] |
| Phi of -K* | [-2,-1,0,0,1,2,1,0,2,2,0,1,2,1,1,-1,-1,1,-1,2,1] |
| Symmetry type of based matrix | c |
| u-polynomial | 0 |
| Normalized Jones-Krushkal polynomial | 5z^2+18z+17 |
| Enhanced Jones-Krushkal polynomial | -4w^4z^2+9w^3z^2-8w^3z+26w^2z+17w |
| Inner characteristic polynomial | t^6+25t^4+20t^2 |
| Outer characteristic polynomial | t^7+35t^5+110t^3+15t |
| Flat arrow polynomial | 4*K1**3 - 4*K1**2 - 4*K1*K2 - K1 + 2*K2 + K3 + 3 |
| 2-strand cable arrow polynomial | -128*K1**4*K2**2 + 192*K1**4*K2 - 208*K1**4 + 64*K1**3*K2*K3 - 96*K1**3*K3 - 1536*K1**2*K2**4 + 3840*K1**2*K2**3 + 64*K1**2*K2**2*K4 - 8208*K1**2*K2**2 - 96*K1**2*K2*K4 + 5920*K1**2*K2 - 16*K1**2*K3**2 - 3840*K1**2 + 2656*K1*K2**3*K3 - 2112*K1*K2**2*K3 - 384*K1*K2**2*K5 - 32*K1*K2*K3*K4 + 5816*K1*K2*K3 + 88*K1*K3*K4 - 32*K2**6 + 64*K2**4*K4 - 4192*K2**4 - 32*K2**3*K6 - 944*K2**2*K3**2 - 16*K2**2*K4**2 + 2352*K2**2*K4 - 702*K2**2 + 232*K2*K3*K5 + 16*K2*K4*K6 - 1252*K3**2 - 144*K4**2 - 20*K5**2 - 2*K6**2 + 2686 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {2, 5}, {3, 4}], [{1, 6}, {3, 5}, {2, 4}], [{1, 6}, {4, 5}, {2, 3}]] |
| If K is slice | False |