| Min(phi) over symmetries of the knot is: [-2,-1,-1,1,1,2,-1,1,2,2,3,0,1,2,0,2,2,2,0,1,1] |
| Flat knots (up to 7 crossings) with same phi are :['6.1512'] |
| Arrow polynomial of the knot is: -12*K1**2 - 4*K1*K2 + 2*K1 + 6*K2 + 2*K3 + 7 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.546', '6.591', '6.598', '6.666', '6.680', '6.742', '6.778', '6.805', '6.822', '6.824', '6.1129', '6.1512', '6.1647', '6.1678', '6.1705', '6.1847', '6.1857'] |
| Outer characteristic polynomial of the knot is: t^7+30t^5+59t^3+5t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1512'] |
| 2-strand cable arrow polynomial of the knot is: -448*K1**6 - 320*K1**4*K2**2 + 1248*K1**4*K2 - 3552*K1**4 + 608*K1**3*K2*K3 + 32*K1**3*K3*K4 - 544*K1**3*K3 - 3856*K1**2*K2**2 - 416*K1**2*K2*K4 + 7528*K1**2*K2 - 640*K1**2*K3**2 - 176*K1**2*K4**2 - 3788*K1**2 - 704*K1*K2**2*K3 - 32*K1*K2*K3*K4 + 5416*K1*K2*K3 + 1344*K1*K3*K4 + 232*K1*K4*K5 - 272*K2**4 - 208*K2**2*K3**2 - 48*K2**2*K4**2 + 888*K2**2*K4 - 3700*K2**2 + 176*K2*K3*K5 + 32*K2*K4*K6 - 1796*K3**2 - 688*K4**2 - 104*K5**2 - 4*K6**2 + 3790 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1512'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.4127', 'vk6.4160', 'vk6.5369', 'vk6.5402', 'vk6.7495', 'vk6.7524', 'vk6.9000', 'vk6.9033', 'vk6.12444', 'vk6.12477', 'vk6.13339', 'vk6.13562', 'vk6.13595', 'vk6.14248', 'vk6.14697', 'vk6.14740', 'vk6.15198', 'vk6.15855', 'vk6.15900', 'vk6.30853', 'vk6.30886', 'vk6.32041', 'vk6.32074', 'vk6.33055', 'vk6.33088', 'vk6.33857', 'vk6.34316', 'vk6.48475', 'vk6.50260', 'vk6.53527', 'vk6.53946', 'vk6.54273'] |
| 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 | O1O2O3U2O4U1U4O5O6U5U3U6 |
| R3 orbit | {'O1O2O3U2O4U1U4O5O6U5U3U6'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U4U1U5O4O5U6U3O6U2 |
| Gauss code of K* | O1O2O3U4U5U2O5U6O4O6U1U3 |
| Gauss code of -K* | O1O2O3U1U3O4O5U4O6U2U6U5 |
| 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 -1 2],[ 2 0 0 3 1 0 1],[ 1 0 0 1 0 0 1],[-1 -3 -1 0 0 0 2],[-1 -1 0 0 0 0 0],[ 1 0 0 0 0 0 1],[-2 -1 -1 -2 0 -1 0]] |
| Primitive based matrix | [[ 0 2 1 1 -1 -1 -2],[-2 0 0 -2 -1 -1 -1],[-1 0 0 0 0 0 -1],[-1 2 0 0 0 -1 -3],[ 1 1 0 0 0 0 0],[ 1 1 0 1 0 0 0],[ 2 1 1 3 0 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,-1,1,1,2,0,2,1,1,1,0,0,0,1,0,1,3,0,0,0] |
| Phi over symmetry | [-2,-1,-1,1,1,2,-1,1,2,2,3,0,1,2,0,2,2,2,0,1,1] |
| Phi of -K | [-2,-1,-1,1,1,2,1,1,0,2,3,0,1,2,2,2,2,2,0,-1,1] |
| Phi of K* | [-2,-1,-1,1,1,2,-1,1,2,2,3,0,1,2,0,2,2,2,0,1,1] |
| Phi of -K* | [-2,-1,-1,1,1,2,0,0,1,3,1,0,0,0,1,0,1,1,0,0,2] |
| Symmetry type of based matrix | c |
| u-polynomial | 0 |
| Normalized Jones-Krushkal polynomial | 17z+35 |
| Enhanced Jones-Krushkal polynomial | 17w^2z+35w |
| Inner characteristic polynomial | t^6+18t^4+21t^2+1 |
| Outer characteristic polynomial | t^7+30t^5+59t^3+5t |
| Flat arrow polynomial | -12*K1**2 - 4*K1*K2 + 2*K1 + 6*K2 + 2*K3 + 7 |
| 2-strand cable arrow polynomial | -448*K1**6 - 320*K1**4*K2**2 + 1248*K1**4*K2 - 3552*K1**4 + 608*K1**3*K2*K3 + 32*K1**3*K3*K4 - 544*K1**3*K3 - 3856*K1**2*K2**2 - 416*K1**2*K2*K4 + 7528*K1**2*K2 - 640*K1**2*K3**2 - 176*K1**2*K4**2 - 3788*K1**2 - 704*K1*K2**2*K3 - 32*K1*K2*K3*K4 + 5416*K1*K2*K3 + 1344*K1*K3*K4 + 232*K1*K4*K5 - 272*K2**4 - 208*K2**2*K3**2 - 48*K2**2*K4**2 + 888*K2**2*K4 - 3700*K2**2 + 176*K2*K3*K5 + 32*K2*K4*K6 - 1796*K3**2 - 688*K4**2 - 104*K5**2 - 4*K6**2 + 3790 |
| Genus of based matrix | 0 |
| Fillings of based matrix | [[{1, 6}, {4, 5}, {2, 3}]] |
| If K is slice | True |