| Min(phi) over symmetries of the knot is: [-3,-2,0,1,2,2,0,0,3,3,4,0,2,1,2,0,1,1,1,1,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.905'] |
| 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+69t^5+98t^3+5t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.905'] |
| 2-strand cable arrow polynomial of the knot is: -1536*K1**2*K2**2 + 32*K1**2*K2*K3*K5 + 2296*K1**2*K2 - 64*K1**2*K3**2 - 64*K1**2*K5**2 - 2464*K1**2 - 128*K1*K2**2*K3 - 128*K1*K2**2*K5 - 288*K1*K2*K3*K4 - 64*K1*K2*K3*K6 + 2616*K1*K2*K3 - 160*K1*K2*K4*K5 + 544*K1*K3*K4 + 440*K1*K4*K5 + 152*K1*K5*K6 - 440*K2**4 - 544*K2**2*K3**2 - 168*K2**2*K4**2 + 1040*K2**2*K4 - 2174*K2**2 + 992*K2*K3*K5 + 240*K2*K4*K6 + 8*K3**2*K6 - 1168*K3**2 - 722*K4**2 - 472*K5**2 - 90*K6**2 + 2312 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.905'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.4232', 'vk6.4311', 'vk6.5501', 'vk6.5617', 'vk6.7608', 'vk6.7697', 'vk6.9101', 'vk6.9180', 'vk6.18372', 'vk6.18712', 'vk6.24825', 'vk6.25284', 'vk6.37013', 'vk6.37463', 'vk6.44186', 'vk6.44507', 'vk6.48552', 'vk6.48607', 'vk6.49257', 'vk6.49375', 'vk6.50349', 'vk6.50404', 'vk6.51082', 'vk6.51113', 'vk6.56145', 'vk6.56374', 'vk6.60670', 'vk6.61019', 'vk6.65809', 'vk6.66063', 'vk6.68806', 'vk6.69016'] |
| 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 | O1O2O3O4U2U5O6O5U1U6U4U3 |
| R3 orbit | {'O1O2O3O4U2U5O6O5U1U6U4U3'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U2U1U5U4O6O5U6U3 |
| Gauss code of K* | O1O2O3O4U1U5U4U3O5O6U2U6 |
| Gauss code of -K* | O1O2O3O4U5U3O5O6U2U1U6U4 |
| 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 -2 2 2 1 0],[ 3 0 0 4 3 3 0],[ 2 0 0 2 1 2 0],[-2 -4 -2 0 0 -1 -1],[-2 -3 -1 0 0 -1 -1],[-1 -3 -2 1 1 0 0],[ 0 0 0 1 1 0 0]] |
| Primitive based matrix | [[ 0 2 2 1 0 -2 -3],[-2 0 0 -1 -1 -1 -3],[-2 0 0 -1 -1 -2 -4],[-1 1 1 0 0 -2 -3],[ 0 1 1 0 0 0 0],[ 2 1 2 2 0 0 0],[ 3 3 4 3 0 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-2,-1,0,2,3,0,1,1,1,3,1,1,2,4,0,2,3,0,0,0] |
| Phi over symmetry | [-3,-2,0,1,2,2,0,0,3,3,4,0,2,1,2,0,1,1,1,1,0] |
| Phi of -K | [-3,-2,0,1,2,2,1,3,1,1,2,2,1,2,3,1,1,1,0,0,0] |
| Phi of K* | [-2,-2,-1,0,2,3,0,0,1,2,1,0,1,3,2,1,1,1,2,3,1] |
| Phi of -K* | [-3,-2,0,1,2,2,0,0,3,3,4,0,2,1,2,0,1,1,1,1,0] |
| Symmetry type of based matrix | c |
| u-polynomial | t^3-t^2-t |
| Normalized Jones-Krushkal polynomial | 7z^2+24z+21 |
| Enhanced Jones-Krushkal polynomial | 7w^3z^2+24w^2z+21w |
| Inner characteristic polynomial | t^6+47t^4+47t^2+1 |
| Outer characteristic polynomial | t^7+69t^5+98t^3+5t |
| Flat arrow polynomial | -2*K1**2 - 2*K1*K2 + K1 + K2 + K3 + 2 |
| 2-strand cable arrow polynomial | -1536*K1**2*K2**2 + 32*K1**2*K2*K3*K5 + 2296*K1**2*K2 - 64*K1**2*K3**2 - 64*K1**2*K5**2 - 2464*K1**2 - 128*K1*K2**2*K3 - 128*K1*K2**2*K5 - 288*K1*K2*K3*K4 - 64*K1*K2*K3*K6 + 2616*K1*K2*K3 - 160*K1*K2*K4*K5 + 544*K1*K3*K4 + 440*K1*K4*K5 + 152*K1*K5*K6 - 440*K2**4 - 544*K2**2*K3**2 - 168*K2**2*K4**2 + 1040*K2**2*K4 - 2174*K2**2 + 992*K2*K3*K5 + 240*K2*K4*K6 + 8*K3**2*K6 - 1168*K3**2 - 722*K4**2 - 472*K5**2 - 90*K6**2 + 2312 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{2, 6}, {1, 5}, {3, 4}], [{3, 6}, {4, 5}, {1, 2}], [{4, 6}, {2, 5}, {1, 3}]] |
| If K is slice | False |