| Min(phi) over symmetries of the knot is: [-3,-2,0,1,2,2,-1,0,3,3,3,1,3,1,2,1,0,1,1,1,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.854'] |
| 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+63t^5+120t^3+8t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.854'] |
| 2-strand cable arrow polynomial of the knot is: -144*K1**4 + 384*K1**3*K2*K3 - 160*K1**3*K3 - 256*K1**2*K2**2*K3**2 - 2080*K1**2*K2**2 + 128*K1**2*K2*K3**2 + 32*K1**2*K2*K3*K5 - 448*K1**2*K2*K4 + 3040*K1**2*K2 - 272*K1**2*K3**2 - 2628*K1**2 + 288*K1*K2**3*K3 + 896*K1*K2**2*K3*K4 - 1056*K1*K2**2*K3 - 32*K1*K2**2*K5 - 416*K1*K2*K3*K4 - 64*K1*K2*K3*K6 + 3408*K1*K2*K3 + 944*K1*K3*K4 + 8*K1*K4*K5 - 72*K2**4 - 720*K2**2*K3**2 - 488*K2**2*K4**2 + 1080*K2**2*K4 - 2094*K2**2 + 336*K2*K3*K5 + 80*K2*K4*K6 - 1184*K3**2 - 522*K4**2 - 4*K5**2 - 2*K6**2 + 2016 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.854'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.11420', 'vk6.11711', 'vk6.12728', 'vk6.13077', 'vk6.20614', 'vk6.22033', 'vk6.28087', 'vk6.29535', 'vk6.31161', 'vk6.31498', 'vk6.32319', 'vk6.32749', 'vk6.39498', 'vk6.41712', 'vk6.46096', 'vk6.47750', 'vk6.52174', 'vk6.52414', 'vk6.52997', 'vk6.53319', 'vk6.57490', 'vk6.58667', 'vk6.62170', 'vk6.63127', 'vk6.63745', 'vk6.63849', 'vk6.64167', 'vk6.64360', 'vk6.67012', 'vk6.67883', 'vk6.69634', 'vk6.70320'] |
| 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 | O1O2O3O4U1U4O5O6U2U3U6U5 |
| R3 orbit | {'O1O2O3O4U1U4O5O6U2U3U6U5'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U5U6U2U3O6O5U1U4 |
| Gauss code of K* | O1O2O3O4U5U1U2U6O5O6U4U3 |
| Gauss code of -K* | O1O2O3O4U2U1O5O6U5U3U4U6 |
| 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 0 1 2 2],[ 3 0 2 3 1 2 2],[ 2 -2 0 1 0 3 2],[ 0 -3 -1 0 0 2 1],[-1 -1 0 0 0 0 0],[-2 -2 -3 -2 0 0 0],[-2 -2 -2 -1 0 0 0]] |
| Primitive based matrix | [[ 0 2 2 1 0 -2 -3],[-2 0 0 0 -1 -2 -2],[-2 0 0 0 -2 -3 -2],[-1 0 0 0 0 0 -1],[ 0 1 2 0 0 -1 -3],[ 2 2 3 0 1 0 -2],[ 3 2 2 1 3 2 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-2,-1,0,2,3,0,0,1,2,2,0,2,3,2,0,0,1,1,3,2] |
| Phi over symmetry | [-3,-2,0,1,2,2,-1,0,3,3,3,1,3,1,2,1,0,1,1,1,0] |
| Phi of -K | [-3,-2,0,1,2,2,-1,0,3,3,3,1,3,1,2,1,0,1,1,1,0] |
| Phi of K* | [-2,-2,-1,0,2,3,0,1,0,1,3,1,1,2,3,1,3,3,1,0,-1] |
| Phi of -K* | [-3,-2,0,1,2,2,2,3,1,2,2,1,0,2,3,0,1,2,0,0,0] |
| 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+41t^4+41t^2+1 |
| Outer characteristic polynomial | t^7+63t^5+120t^3+8t |
| Flat arrow polynomial | -2*K1**2 - 2*K1*K2 + K1 + K2 + K3 + 2 |
| 2-strand cable arrow polynomial | -144*K1**4 + 384*K1**3*K2*K3 - 160*K1**3*K3 - 256*K1**2*K2**2*K3**2 - 2080*K1**2*K2**2 + 128*K1**2*K2*K3**2 + 32*K1**2*K2*K3*K5 - 448*K1**2*K2*K4 + 3040*K1**2*K2 - 272*K1**2*K3**2 - 2628*K1**2 + 288*K1*K2**3*K3 + 896*K1*K2**2*K3*K4 - 1056*K1*K2**2*K3 - 32*K1*K2**2*K5 - 416*K1*K2*K3*K4 - 64*K1*K2*K3*K6 + 3408*K1*K2*K3 + 944*K1*K3*K4 + 8*K1*K4*K5 - 72*K2**4 - 720*K2**2*K3**2 - 488*K2**2*K4**2 + 1080*K2**2*K4 - 2094*K2**2 + 336*K2*K3*K5 + 80*K2*K4*K6 - 1184*K3**2 - 522*K4**2 - 4*K5**2 - 2*K6**2 + 2016 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{3, 6}, {1, 5}, {2, 4}], [{5, 6}, {2, 4}, {1, 3}]] |
| If K is slice | False |