| Min(phi) over symmetries of the knot is: [-3,-1,0,1,1,2,1,0,3,3,3,-1,1,1,2,-1,0,2,0,1,1] |
| Flat knots (up to 7 crossings) with same phi are :['6.1139'] |
| 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+44t^5+128t^3+8t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1139'] |
| 2-strand cable arrow polynomial of the knot is: -1600*K1**2*K2**2 - 32*K1**2*K2*K4 + 2416*K1**2*K2 - 2416*K1**2 + 448*K1*K2**3*K3 + 160*K1*K2**2*K3*K4 - 544*K1*K2**2*K3 - 64*K1*K2**2*K5 - 384*K1*K2*K3*K4 + 2872*K1*K2*K3 + 520*K1*K3*K4 + 208*K1*K4*K5 - 984*K2**4 - 1088*K2**2*K3**2 - 200*K2**2*K4**2 + 1392*K2**2*K4 - 1790*K2**2 + 856*K2*K3*K5 + 64*K2*K4*K6 - 1128*K3**2 - 586*K4**2 - 224*K5**2 - 2*K6**2 + 2104 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1139'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.17029', 'vk6.17272', 'vk6.20560', 'vk6.21963', 'vk6.23458', 'vk6.23755', 'vk6.28019', 'vk6.29483', 'vk6.35534', 'vk6.35984', 'vk6.39429', 'vk6.41625', 'vk6.42946', 'vk6.43241', 'vk6.46011', 'vk6.47683', 'vk6.55209', 'vk6.55444', 'vk6.57433', 'vk6.58602', 'vk6.59607', 'vk6.59926', 'vk6.62103', 'vk6.63078', 'vk6.65015', 'vk6.65222', 'vk6.66970', 'vk6.67832', 'vk6.68288', 'vk6.68441', 'vk6.69585', 'vk6.70280'] |
| 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 | O1O2O3O4U1U2U4O5O6U3U6U5 |
| R3 orbit | {'O1O2O3O4U1U2U4O5O6U3U6U5'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U5U6U2O6O5U1U3U4 |
| Gauss code of K* | O1O2O3U4U5O6O5O4U1U2U6U3 |
| Gauss code of -K* | O1O2O3U2U1O4O5O6U4U3U5U6 |
| 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 1 3 2 1 1],[ 1 -1 0 2 1 1 1],[ 0 -3 -2 0 0 2 1],[-2 -2 -1 0 0 0 0],[-1 -1 -1 -2 0 0 0],[-1 -1 -1 -1 0 0 0]] |
| Primitive based matrix | [[ 0 2 1 1 0 -1 -3],[-2 0 0 0 0 -1 -2],[-1 0 0 0 -1 -1 -1],[-1 0 0 0 -2 -1 -1],[ 0 0 1 2 0 -2 -3],[ 1 1 1 1 2 0 -1],[ 3 2 1 1 3 1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,-1,0,1,3,0,0,0,1,2,0,1,1,1,2,1,1,2,3,1] |
| Phi over symmetry | [-3,-1,0,1,1,2,1,0,3,3,3,-1,1,1,2,-1,0,2,0,1,1] |
| Phi of -K | [-3,-1,0,1,1,2,1,0,3,3,3,-1,1,1,2,-1,0,2,0,1,1] |
| Phi of K* | [-2,-1,-1,0,1,3,1,1,2,2,3,0,-1,1,3,0,1,3,-1,0,1] |
| Phi of -K* | [-3,-1,0,1,1,2,1,3,1,1,2,2,1,1,1,1,2,0,0,0,0] |
| Symmetry type of based matrix | c |
| u-polynomial | t^3-t^2-t |
| Normalized Jones-Krushkal polynomial | 6z^2+19z+15 |
| Enhanced Jones-Krushkal polynomial | -4w^4z^2+10w^3z^2-4w^3z+23w^2z+15w |
| Inner characteristic polynomial | t^6+28t^4+31t^2+1 |
| Outer characteristic polynomial | t^7+44t^5+128t^3+8t |
| Flat arrow polynomial | -2*K1**2 - 2*K1*K2 + K1 + K2 + K3 + 2 |
| 2-strand cable arrow polynomial | -1600*K1**2*K2**2 - 32*K1**2*K2*K4 + 2416*K1**2*K2 - 2416*K1**2 + 448*K1*K2**3*K3 + 160*K1*K2**2*K3*K4 - 544*K1*K2**2*K3 - 64*K1*K2**2*K5 - 384*K1*K2*K3*K4 + 2872*K1*K2*K3 + 520*K1*K3*K4 + 208*K1*K4*K5 - 984*K2**4 - 1088*K2**2*K3**2 - 200*K2**2*K4**2 + 1392*K2**2*K4 - 1790*K2**2 + 856*K2*K3*K5 + 64*K2*K4*K6 - 1128*K3**2 - 586*K4**2 - 224*K5**2 - 2*K6**2 + 2104 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {2, 5}, {3, 4}], [{3, 6}, {2, 5}, {1, 4}], [{4, 6}, {1, 5}, {2, 3}], [{4, 6}, {2, 5}, {1, 3}]] |
| If K is slice | False |