| Min(phi) over symmetries of the knot is: [-3,-1,0,1,1,2,0,2,2,3,2,1,1,1,1,0,0,1,-1,1,2] |
| Flat knots (up to 7 crossings) with same phi are :['6.219'] |
| 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+46t^5+40t^3 |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.219', '6.860'] |
| 2-strand cable arrow polynomial of the knot is: -64*K1**6 + 64*K1**4*K2 - 400*K1**4 - 144*K1**2*K2**2 + 528*K1**2*K2 - 112*K1**2*K3**2 - 48*K1**2*K4**2 - 284*K1**2 + 424*K1*K2*K3 + 240*K1*K3*K4 + 40*K1*K4*K5 - 8*K2**4 - 16*K2**2*K3**2 - 8*K2**2*K4**2 + 40*K2**2*K4 - 318*K2**2 + 24*K2*K3*K5 + 8*K2*K4*K6 - 236*K3**2 - 106*K4**2 - 16*K5**2 - 2*K6**2 + 392 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.219'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.4062', 'vk6.4070', 'vk6.4093', 'vk6.4101', 'vk6.5300', 'vk6.5308', 'vk6.5331', 'vk6.5339', 'vk6.5516', 'vk6.5524', 'vk6.5635', 'vk6.5643', 'vk6.7453', 'vk6.7461', 'vk6.8923', 'vk6.8931', 'vk6.8954', 'vk6.8962', 'vk6.14562', 'vk6.14563', 'vk6.15292', 'vk6.15294', 'vk6.15781', 'vk6.15782', 'vk6.16197', 'vk6.16198', 'vk6.29844', 'vk6.29848', 'vk6.29875', 'vk6.29879', 'vk6.33928', 'vk6.33930', 'vk6.34229', 'vk6.34230', 'vk6.38234', 'vk6.38235', 'vk6.45007', 'vk6.45008', 'vk6.49266', 'vk6.49274', 'vk6.50227', 'vk6.50235', 'vk6.51590', 'vk6.51594', 'vk6.53971', 'vk6.53973', 'vk6.54474', 'vk6.54476'] |
| 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 | O1O2O3O4O5U2O6U5U6U4U1U3 |
| R3 orbit | {'O1O2O3O4O5U2O6U5U6U4U1U3', 'O1O2O3O4O5U2U4O6U5U6U1U3', 'O1O2O3O4U1O5U4U5U6U2O6U3'} |
| R3 orbit length | 3 |
| Gauss code of -K | O1O2O3O4O5U3U5U2U6U1O6U4 |
| Gauss code of K* | O1O2O3O4O5U4U6U5U3U1O6U2 |
| Gauss code of -K* | O1O2O3O4O5U4O6U5U3U1U6U2 |
| Diagrammatic symmetry type | c |
| Flat genus of the diagram | 2 |
| If K is checkerboard colorable | False |
| If K is almost classical | False |
| Based matrix from Gauss code | [[ 0 -1 -3 2 1 0 1],[ 1 0 -2 2 1 0 1],[ 3 2 0 3 2 1 1],[-2 -2 -3 0 0 -1 1],[-1 -1 -2 0 0 -1 1],[ 0 0 -1 1 1 0 1],[-1 -1 -1 -1 -1 -1 0]] |
| Primitive based matrix | [[ 0 2 1 1 0 -1 -3],[-2 0 1 0 -1 -2 -3],[-1 -1 0 -1 -1 -1 -1],[-1 0 1 0 -1 -1 -2],[ 0 1 1 1 0 0 -1],[ 1 2 1 1 0 0 -2],[ 3 3 1 2 1 2 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,-1,0,1,3,-1,0,1,2,3,1,1,1,1,1,1,2,0,1,2] |
| Phi over symmetry | [-3,-1,0,1,1,2,0,2,2,3,2,1,1,1,1,0,0,1,-1,1,2] |
| Phi of -K | [-3,-1,0,1,1,2,0,2,2,3,2,1,1,1,1,0,0,1,-1,1,2] |
| Phi of K* | [-2,-1,-1,0,1,3,1,2,1,1,2,1,0,1,2,0,1,3,1,2,0] |
| Phi of -K* | [-3,-1,0,1,1,2,2,1,1,2,3,0,1,1,2,1,1,1,-1,-1,0] |
| Symmetry type of based matrix | c |
| u-polynomial | t^3-t^2-t |
| Normalized Jones-Krushkal polynomial | 7z+15 |
| Enhanced Jones-Krushkal polynomial | 7w^2z+15w |
| Inner characteristic polynomial | t^6+30t^4+11t^2 |
| Outer characteristic polynomial | t^7+46t^5+40t^3 |
| Flat arrow polynomial | -2*K1**2 - 2*K1*K2 + K1 + K2 + K3 + 2 |
| 2-strand cable arrow polynomial | -64*K1**6 + 64*K1**4*K2 - 400*K1**4 - 144*K1**2*K2**2 + 528*K1**2*K2 - 112*K1**2*K3**2 - 48*K1**2*K4**2 - 284*K1**2 + 424*K1*K2*K3 + 240*K1*K3*K4 + 40*K1*K4*K5 - 8*K2**4 - 16*K2**2*K3**2 - 8*K2**2*K4**2 + 40*K2**2*K4 - 318*K2**2 + 24*K2*K3*K5 + 8*K2*K4*K6 - 236*K3**2 - 106*K4**2 - 16*K5**2 - 2*K6**2 + 392 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{4, 6}, {1, 5}, {2, 3}], [{5, 6}, {2, 4}, {1, 3}], [{5, 6}, {4}, {1, 3}, {2}]] |
| If K is slice | False |