| Min(phi) over symmetries of the knot is: [-3,-1,-1,1,2,2,0,2,1,2,4,1,0,0,1,1,2,3,0,0,-1] |
| Flat knots (up to 7 crossings) with same phi are :['6.772'] |
| Arrow polynomial of the knot is: -8*K1**2 - 2*K1*K2 + K1 + 4*K2 + K3 + 5 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.377', '6.638', '6.646', '6.647', '6.657', '6.658', '6.662', '6.692', '6.695', '6.714', '6.720', '6.726', '6.730', '6.731', '6.749', '6.756', '6.772', '6.779', '6.781', '6.800', '6.829', '6.1085', '6.1089', '6.1302', '6.1349', '6.1350', '6.1360', '6.1362', '6.1375', '6.1384'] |
| Outer characteristic polynomial of the knot is: t^7+66t^5+33t^3+3t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.772'] |
| 2-strand cable arrow polynomial of the knot is: -128*K1**6 + 480*K1**4*K2 - 2272*K1**4 + 256*K1**3*K2*K3 + 64*K1**3*K3*K4 - 800*K1**3*K3 - 1200*K1**2*K2**2 - 160*K1**2*K2*K4 + 4112*K1**2*K2 - 704*K1**2*K3**2 - 80*K1**2*K4**2 - 1928*K1**2 - 32*K1*K2*K3*K4 + 2584*K1*K2*K3 + 568*K1*K3*K4 + 40*K1*K4*K5 - 64*K2**4 - 48*K2**2*K3**2 - 8*K2**2*K4**2 + 120*K2**2*K4 - 1694*K2**2 + 40*K2*K3*K5 + 8*K2*K4*K6 - 784*K3**2 - 140*K4**2 - 8*K5**2 - 2*K6**2 + 1778 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.772'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.4467', 'vk6.4564', 'vk6.5853', 'vk6.5982', 'vk6.6399', 'vk6.6832', 'vk6.8019', 'vk6.8368', 'vk6.9332', 'vk6.9453', 'vk6.11636', 'vk6.11989', 'vk6.12978', 'vk6.13428', 'vk6.13525', 'vk6.13712', 'vk6.14085', 'vk6.15056', 'vk6.15178', 'vk6.17779', 'vk6.17810', 'vk6.18829', 'vk6.19415', 'vk6.19708', 'vk6.24322', 'vk6.25424', 'vk6.25455', 'vk6.26587', 'vk6.33270', 'vk6.33331', 'vk6.37556', 'vk6.39271', 'vk6.39758', 'vk6.41449', 'vk6.44872', 'vk6.46318', 'vk6.47893', 'vk6.48656', 'vk6.49890', 'vk6.53227'] |
| 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 | O1O2O3O4U3O5U1U6U5O6U4U2 |
| R3 orbit | {'O1O2O3U2O4O5U1U6U5O6U3U4', 'O1O2O3O4U3O5U1U6U5O6U4U2'} |
| R3 orbit length | 2 |
| Gauss code of -K | O1O2O3O4U3U1O5U6U5U4O6U2 |
| Gauss code of K* | O1O2O3U2O4O5U1U5U6U4O6U3 |
| Gauss code of -K* | O1O2O3U1O4U5U4U6U3O6O5U2 |
| 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 1 -1 2 2 -1],[ 3 0 3 0 3 1 2],[-1 -3 0 -1 1 1 -2],[ 1 0 1 0 1 0 1],[-2 -3 -1 -1 0 1 -3],[-2 -1 -1 0 -1 0 -2],[ 1 -2 2 -1 3 2 0]] |
| Primitive based matrix | [[ 0 2 2 1 -1 -1 -3],[-2 0 1 -1 -1 -3 -3],[-2 -1 0 -1 0 -2 -1],[-1 1 1 0 -1 -2 -3],[ 1 1 0 1 0 1 0],[ 1 3 2 2 -1 0 -2],[ 3 3 1 3 0 2 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-2,-1,1,1,3,-1,1,1,3,3,1,0,2,1,1,2,3,-1,0,2] |
| Phi over symmetry | [-3,-1,-1,1,2,2,0,2,1,2,4,1,0,0,1,1,2,3,0,0,-1] |
| Phi of -K | [-3,-1,-1,1,2,2,0,2,1,2,4,1,0,0,1,1,2,3,0,0,-1] |
| Phi of K* | [-2,-2,-1,1,1,3,-1,0,1,3,4,0,0,2,2,0,1,1,-1,0,2] |
| Phi of -K* | [-3,-1,-1,1,2,2,0,2,3,1,3,1,1,0,1,2,2,3,1,1,-1] |
| Symmetry type of based matrix | c |
| u-polynomial | t^3-2t^2+t |
| Normalized Jones-Krushkal polynomial | 13z+27 |
| Enhanced Jones-Krushkal polynomial | 13w^2z+27w |
| Inner characteristic polynomial | t^6+46t^4+15t^2 |
| Outer characteristic polynomial | t^7+66t^5+33t^3+3t |
| Flat arrow polynomial | -8*K1**2 - 2*K1*K2 + K1 + 4*K2 + K3 + 5 |
| 2-strand cable arrow polynomial | -128*K1**6 + 480*K1**4*K2 - 2272*K1**4 + 256*K1**3*K2*K3 + 64*K1**3*K3*K4 - 800*K1**3*K3 - 1200*K1**2*K2**2 - 160*K1**2*K2*K4 + 4112*K1**2*K2 - 704*K1**2*K3**2 - 80*K1**2*K4**2 - 1928*K1**2 - 32*K1*K2*K3*K4 + 2584*K1*K2*K3 + 568*K1*K3*K4 + 40*K1*K4*K5 - 64*K2**4 - 48*K2**2*K3**2 - 8*K2**2*K4**2 + 120*K2**2*K4 - 1694*K2**2 + 40*K2*K3*K5 + 8*K2*K4*K6 - 784*K3**2 - 140*K4**2 - 8*K5**2 - 2*K6**2 + 1778 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{2, 6}, {1, 5}, {3, 4}], [{2, 6}, {3, 5}, {1, 4}], [{2, 6}, {4, 5}, {1, 3}], [{4, 6}, {2, 5}, {1, 3}], [{6}, {1, 5}, {3, 4}, {2}]] |
| If K is slice | False |