| Min(phi) over symmetries of the knot is: [-3,-2,1,1,1,2,0,2,3,3,2,1,2,2,1,-1,0,0,0,2,1] |
| Flat knots (up to 7 crossings) with same phi are :['6.442'] |
| Arrow polynomial of the knot is: -4*K1**2 - 2*K1*K2 + K1 + 2*K2 + K3 + 3 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.136', '6.207', '6.342', '6.370', '6.376', '6.442', '6.456', '6.539', '6.631', '6.636', '6.674', '6.679', '6.705', '6.740', '6.760', '6.794', '6.795', '6.1369'] |
| Outer characteristic polynomial of the knot is: t^7+62t^5+65t^3 |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.442'] |
| 2-strand cable arrow polynomial of the knot is: -64*K1**6 + 64*K1**4*K2 - 576*K1**4 - 400*K1**2*K2**2 + 800*K1**2*K2 - 288*K1**2*K3**2 - 48*K1**2*K4**2 - 300*K1**2 + 728*K1*K2*K3 + 352*K1*K3*K4 + 40*K1*K4*K5 - 48*K2**4 - 48*K2**2*K3**2 - 8*K2**2*K4**2 + 96*K2**2*K4 - 414*K2**2 + 72*K2*K3*K5 + 8*K2*K4*K6 - 300*K3**2 - 136*K4**2 - 32*K5**2 - 2*K6**2 + 502 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.442'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.11257', 'vk6.11337', 'vk6.12518', 'vk6.12631', 'vk6.13864', 'vk6.13959', 'vk6.14138', 'vk6.14363', 'vk6.14939', 'vk6.15062', 'vk6.15590', 'vk6.16062', 'vk6.16349', 'vk6.16391', 'vk6.17435', 'vk6.22592', 'vk6.22625', 'vk6.22766', 'vk6.23947', 'vk6.24086', 'vk6.24180', 'vk6.25973', 'vk6.26139', 'vk6.26365', 'vk6.28315', 'vk6.30931', 'vk6.31056', 'vk6.31227', 'vk6.31578', 'vk6.33683', 'vk6.34640', 'vk6.34711', 'vk6.34729', 'vk6.35557', 'vk6.36008', 'vk6.36247', 'vk6.37643', 'vk6.38090', 'vk6.39943', 'vk6.40124', 'vk6.42270', 'vk6.44554', 'vk6.44576', 'vk6.44800', 'vk6.52007', 'vk6.54399', 'vk6.56530', 'vk6.59052', 'vk6.59150', 'vk6.64567'] |
| 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 | O1O2O3O4O5U6U2O6U3U5U1U4 |
| R3 orbit | {'O1O2O3O4O5U6U2O6U3U5U1U4', 'O1O2O3O4U5U1O5U2U6U3O6U4', 'O1O2O3O4U2U5U1O5U6U3O6U4', 'O1O2O3O4O5U3U6U2O6U5U1U4'} |
| R3 orbit length | 4 |
| Gauss code of -K | O1O2O3O4O5U2U5U1U3O6U4U6 |
| Gauss code of K* | O1O2O3O4U3U5U1U4U2O6O5U6 |
| Gauss code of -K* | O1O2O3O4U5O6O5U3U1U4U6U2 |
| 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 -2 -1 3 2 -1],[ 1 0 -1 0 3 2 0],[ 2 1 0 0 2 1 2],[ 1 0 0 0 2 1 1],[-3 -3 -2 -2 0 0 -3],[-2 -2 -1 -1 0 0 -2],[ 1 0 -2 -1 3 2 0]] |
| Primitive based matrix | [[ 0 3 2 -1 -1 -1 -2],[-3 0 0 -2 -3 -3 -2],[-2 0 0 -1 -2 -2 -1],[ 1 2 1 0 1 0 0],[ 1 3 2 -1 0 0 -2],[ 1 3 2 0 0 0 -1],[ 2 2 1 0 2 1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-3,-2,1,1,1,2,0,2,3,3,2,1,2,2,1,-1,0,0,0,2,1] |
| Phi over symmetry | [-3,-2,1,1,1,2,0,2,3,3,2,1,2,2,1,-1,0,0,0,2,1] |
| Phi of -K | [-2,-1,-1,-1,2,3,-1,0,1,3,3,0,1,1,1,0,1,1,2,2,1] |
| Phi of K* | [-3,-2,1,1,1,2,1,1,1,2,3,1,1,2,3,0,-1,-1,0,0,1] |
| Phi of -K* | [-2,-1,-1,-1,2,3,0,1,2,1,2,0,1,1,2,0,2,3,2,3,0] |
| Symmetry type of based matrix | c |
| u-polynomial | -t^3+3t |
| Normalized Jones-Krushkal polynomial | 8z+17 |
| Enhanced Jones-Krushkal polynomial | 8w^2z+17w |
| Inner characteristic polynomial | t^6+42t^4+41t^2 |
| Outer characteristic polynomial | t^7+62t^5+65t^3 |
| Flat arrow polynomial | -4*K1**2 - 2*K1*K2 + K1 + 2*K2 + K3 + 3 |
| 2-strand cable arrow polynomial | -64*K1**6 + 64*K1**4*K2 - 576*K1**4 - 400*K1**2*K2**2 + 800*K1**2*K2 - 288*K1**2*K3**2 - 48*K1**2*K4**2 - 300*K1**2 + 728*K1*K2*K3 + 352*K1*K3*K4 + 40*K1*K4*K5 - 48*K2**4 - 48*K2**2*K3**2 - 8*K2**2*K4**2 + 96*K2**2*K4 - 414*K2**2 + 72*K2*K3*K5 + 8*K2*K4*K6 - 300*K3**2 - 136*K4**2 - 32*K5**2 - 2*K6**2 + 502 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {2, 5}, {3, 4}], [{1, 6}, {5}, {3, 4}, {2}], [{3, 6}, {2, 5}, {1, 4}], [{3, 6}, {5}, {1, 4}, {2}], [{4, 6}, {2, 5}, {1, 3}], [{4, 6}, {2, 5}, {3}, {1}], [{5, 6}, {2, 4}, {1, 3}], [{5, 6}, {2, 4}, {3}, {1}]] |
| If K is slice | False |