| Min(phi) over symmetries of the knot is: [-3,-1,0,1,1,2,0,2,2,4,2,1,0,1,1,0,1,1,-1,2,2] |
| Flat knots (up to 7 crossings) with same phi are :['6.1086'] |
| 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+48t^5+57t^3+4t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1086'] |
| 2-strand cable arrow polynomial of the knot is: -16*K1**4 + 32*K1**3*K2*K3 - 1024*K1**3*K3 - 288*K1**2*K2**2 + 224*K1**2*K2*K3**2 + 3448*K1**2*K2 - 1072*K1**2*K3**2 - 192*K1**2*K3*K5 - 4580*K1**2 + 96*K1*K2**3*K3 - 608*K1*K2**2*K3 - 96*K1*K2*K3*K4 + 4776*K1*K2*K3 + 1264*K1*K3*K4 + 192*K1*K4*K5 + 24*K1*K5*K6 - 72*K2**4 - 272*K2**2*K3**2 - 8*K2**2*K4**2 + 264*K2**2*K4 - 2886*K2**2 + 248*K2*K3*K5 + 16*K2*K4*K6 - 2024*K3**2 - 378*K4**2 - 132*K5**2 - 18*K6**2 + 3080 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1086'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.11426', 'vk6.11723', 'vk6.12740', 'vk6.13085', 'vk6.20328', 'vk6.21671', 'vk6.27632', 'vk6.29178', 'vk6.31177', 'vk6.31520', 'vk6.32345', 'vk6.32764', 'vk6.39060', 'vk6.41320', 'vk6.45816', 'vk6.47489', 'vk6.52191', 'vk6.52450', 'vk6.53022', 'vk6.53340', 'vk6.57199', 'vk6.58416', 'vk6.61813', 'vk6.62940', 'vk6.63761', 'vk6.63873', 'vk6.64189', 'vk6.64377', 'vk6.66812', 'vk6.67682', 'vk6.69452', 'vk6.70176'] |
| 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 | O1O2O3O4U1U3O5U2U4O6U5U6 |
| R3 orbit | {'O1O2O3O4U1U3O5U2U4O6U5U6'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U5U6O5U1U3O6U2U4 |
| Gauss code of K* | O1O2U3O4O5U6O3O6U1U4U2U5 |
| Gauss code of -K* | O1O2U1O3O4U2O5O6U3U5U4U6 |
| 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 2 1 3 2 0],[ 1 -2 0 0 2 2 1],[ 0 -1 0 0 1 1 0],[-2 -3 -2 -1 0 1 1],[-1 -2 -2 -1 -1 0 1],[-1 0 -1 0 -1 -1 0]] |
| Primitive based matrix | [[ 0 2 1 1 0 -1 -3],[-2 0 1 1 -1 -2 -3],[-1 -1 0 1 -1 -2 -2],[-1 -1 -1 0 0 -1 0],[ 0 1 1 0 0 0 -1],[ 1 2 2 1 0 0 -2],[ 3 3 2 0 1 2 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,-1,0,1,3,-1,-1,1,2,3,-1,1,2,2,0,1,0,0,1,2] |
| Phi over symmetry | [-3,-1,0,1,1,2,0,2,2,4,2,1,0,1,1,0,1,1,-1,2,2] |
| Phi of -K | [-3,-1,0,1,1,2,0,2,2,4,2,1,0,1,1,0,1,1,-1,2,2] |
| Phi of K* | [-2,-1,-1,0,1,3,2,2,1,1,2,-1,1,1,4,0,0,2,1,2,0] |
| Phi of -K* | [-3,-1,0,1,1,2,2,1,0,2,3,0,1,2,2,0,1,1,-1,-1,-1] |
| Symmetry type of based matrix | c |
| u-polynomial | t^3-t^2-t |
| Normalized Jones-Krushkal polynomial | 3z^2+20z+29 |
| Enhanced Jones-Krushkal polynomial | 3w^3z^2+20w^2z+29w |
| Inner characteristic polynomial | t^6+32t^4+8t^2 |
| Outer characteristic polynomial | t^7+48t^5+57t^3+4t |
| Flat arrow polynomial | -2*K1**2 - 2*K1*K2 + K1 + K2 + K3 + 2 |
| 2-strand cable arrow polynomial | -16*K1**4 + 32*K1**3*K2*K3 - 1024*K1**3*K3 - 288*K1**2*K2**2 + 224*K1**2*K2*K3**2 + 3448*K1**2*K2 - 1072*K1**2*K3**2 - 192*K1**2*K3*K5 - 4580*K1**2 + 96*K1*K2**3*K3 - 608*K1*K2**2*K3 - 96*K1*K2*K3*K4 + 4776*K1*K2*K3 + 1264*K1*K3*K4 + 192*K1*K4*K5 + 24*K1*K5*K6 - 72*K2**4 - 272*K2**2*K3**2 - 8*K2**2*K4**2 + 264*K2**2*K4 - 2886*K2**2 + 248*K2*K3*K5 + 16*K2*K4*K6 - 2024*K3**2 - 378*K4**2 - 132*K5**2 - 18*K6**2 + 3080 |
| 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}], [{5, 6}, {1, 4}, {2, 3}]] |
| If K is slice | False |