| Min(phi) over symmetries of the knot is: [-3,-1,0,1,1,2,-1,2,3,3,3,2,0,1,2,1,1,1,0,1,1] |
| Flat knots (up to 7 crossings) with same phi are :['6.1149'] |
| Arrow polynomial of the knot is: -2*K1**2 - 2*K1*K2 + K1 + K2 + K3 + 2 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.217', '6.219', '6.304', '6.349', '6.390', '6.400', '6.416', '6.515', '6.518', '6.530', '6.582', '6.616', '6.629', '6.641', '6.645', '6.702', '6.710', '6.715', '6.729', '6.733', '6.734', '6.802', '6.840', '6.845', '6.854', '6.860', '6.900', '6.905', '6.921', '6.924', '6.979', '6.980', '6.996', '6.1044', '6.1067', '6.1086', '6.1100', '6.1139', '6.1145', '6.1149', '6.1167', '6.1169', '6.1183', '6.1314'] |
| Outer characteristic polynomial of the knot is: t^7+40t^5+104t^3+8t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1149'] |
| 2-strand cable arrow polynomial of the knot is: -16*K1**4 - 1984*K1**2*K2**2 - 160*K1**2*K2*K4 + 2784*K1**2*K2 - 16*K1**2*K3**2 - 2820*K1**2 + 160*K1*K2**3*K3 + 256*K1*K2**2*K3*K4 - 544*K1*K2**2*K3 - 32*K1*K2*K3*K4 - 64*K1*K2*K3*K6 + 3480*K1*K2*K3 + 624*K1*K3*K4 + 8*K1*K5*K6 - 200*K2**4 - 784*K2**2*K3**2 - 488*K2**2*K4**2 + 1264*K2**2*K4 - 2542*K2**2 + 384*K2*K3*K5 + 240*K2*K4*K6 - 1248*K3**2 - 650*K4**2 - 28*K5**2 - 18*K6**2 + 2392 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1149'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.11551', 'vk6.11890', 'vk6.12906', 'vk6.13208', 'vk6.20681', 'vk6.22121', 'vk6.28193', 'vk6.29618', 'vk6.31335', 'vk6.31746', 'vk6.32507', 'vk6.32908', 'vk6.39647', 'vk6.41888', 'vk6.46243', 'vk6.47850', 'vk6.52329', 'vk6.52591', 'vk6.53177', 'vk6.53470', 'vk6.57613', 'vk6.58773', 'vk6.62281', 'vk6.63219', 'vk6.63830', 'vk6.63967', 'vk6.64278', 'vk6.64472', 'vk6.67077', 'vk6.67943', 'vk6.69688', 'vk6.70371'] |
| 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 | O1O2O3O4U1U3U4O5O6U2U6U5 |
| R3 orbit | {'O1O2O3O4U1U3U4O5O6U2U6U5'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U5U6U3O6O5U1U2U4 |
| Gauss code of K* | O1O2O3U4U5O6O5O4U1U6U2U3 |
| Gauss code of -K* | O1O2O3U2U1O4O5O6U4U5U3U6 |
| 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 0 2 1 1],[ 3 0 3 1 2 1 1],[ 1 -3 0 -1 1 2 1],[ 0 -1 1 0 1 0 0],[-2 -2 -1 -1 0 0 0],[-1 -1 -2 0 0 0 0],[-1 -1 -1 0 0 0 0]] |
| Primitive based matrix | [[ 0 2 1 1 0 -1 -3],[-2 0 0 0 -1 -1 -2],[-1 0 0 0 0 -1 -1],[-1 0 0 0 0 -2 -1],[ 0 1 0 0 0 1 -1],[ 1 1 1 2 -1 0 -3],[ 3 2 1 1 1 3 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,-1,0,1,3,0,0,1,1,2,0,0,1,1,0,2,1,-1,1,3] |
| Phi over symmetry | [-3,-1,0,1,1,2,-1,2,3,3,3,2,0,1,2,1,1,1,0,1,1] |
| Phi of -K | [-3,-1,0,1,1,2,-1,2,3,3,3,2,0,1,2,1,1,1,0,1,1] |
| Phi of K* | [-2,-1,-1,0,1,3,1,1,1,2,3,0,1,0,3,1,1,3,2,2,-1] |
| Phi of -K* | [-3,-1,0,1,1,2,3,1,1,1,2,-1,1,2,1,0,0,1,0,0,0] |
| Symmetry type of based matrix | c |
| u-polynomial | t^3-t^2-t |
| Normalized Jones-Krushkal polynomial | 5z^2+18z+17 |
| Enhanced Jones-Krushkal polynomial | -4w^4z^2+9w^3z^2-4w^3z+22w^2z+17w |
| Inner characteristic polynomial | t^6+24t^4+31t^2+1 |
| Outer characteristic polynomial | t^7+40t^5+104t^3+8t |
| Flat arrow polynomial | -2*K1**2 - 2*K1*K2 + K1 + K2 + K3 + 2 |
| 2-strand cable arrow polynomial | -16*K1**4 - 1984*K1**2*K2**2 - 160*K1**2*K2*K4 + 2784*K1**2*K2 - 16*K1**2*K3**2 - 2820*K1**2 + 160*K1*K2**3*K3 + 256*K1*K2**2*K3*K4 - 544*K1*K2**2*K3 - 32*K1*K2*K3*K4 - 64*K1*K2*K3*K6 + 3480*K1*K2*K3 + 624*K1*K3*K4 + 8*K1*K5*K6 - 200*K2**4 - 784*K2**2*K3**2 - 488*K2**2*K4**2 + 1264*K2**2*K4 - 2542*K2**2 + 384*K2*K3*K5 + 240*K2*K4*K6 - 1248*K3**2 - 650*K4**2 - 28*K5**2 - 18*K6**2 + 2392 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{4, 6}, {3, 5}, {1, 2}]] |
| If K is slice | False |