| Min(phi) over symmetries of the knot is: [-2,-2,-1,1,2,2,-1,0,1,2,3,0,1,0,2,0,1,1,0,0,-1] |
| Flat knots (up to 7 crossings) with same phi are :['6.898'] |
| Arrow polynomial of the knot is: -8*K1**2 - 4*K1*K2 + 2*K1 + 4*K2 + 2*K3 + 5 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.235', '6.379', '6.411', '6.547', '6.811', '6.818', '6.823', '6.897', '6.898', '6.1008', '6.1053', '6.1109', '6.1110', '6.1130', '6.1222', '6.1239', '6.1303', '6.1307', '6.1342', '6.1491', '6.1495', '6.1496', '6.1519', '6.1592', '6.1593', '6.1642', '6.1652', '6.1653', '6.1671', '6.1673', '6.1717'] |
| Outer characteristic polynomial of the knot is: t^7+41t^5+53t^3+5t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.898'] |
| 2-strand cable arrow polynomial of the knot is: 64*K1**4*K2 - 1344*K1**4 - 896*K1**3*K3 - 1120*K1**2*K2**2 - 128*K1**2*K2*K4 + 5120*K1**2*K2 - 1088*K1**2*K3**2 - 4792*K1**2 + 64*K1*K2*K3**3 - 128*K1*K2*K3*K4 + 5024*K1*K2*K3 - 64*K1*K3**2*K5 + 1312*K1*K3*K4 + 96*K1*K4*K5 - 64*K2**4 - 320*K2**2*K3**2 - 16*K2**2*K4**2 + 448*K2**2*K4 - 3716*K2**2 + 720*K2*K3*K5 + 32*K2*K4*K6 - 192*K3**4 + 256*K3**2*K6 - 2296*K3**2 - 592*K4**2 - 288*K5**2 - 84*K6**2 + 3990 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.898'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.3566', 'vk6.3588', 'vk6.3813', 'vk6.3846', 'vk6.6975', 'vk6.7008', 'vk6.7197', 'vk6.7229', 'vk6.15345', 'vk6.15470', 'vk6.33984', 'vk6.34034', 'vk6.34440', 'vk6.48212', 'vk6.48374', 'vk6.49945', 'vk6.49966', 'vk6.54010', 'vk6.54058', 'vk6.54504'] |
| The R3 orbit of minmal crossing diagrams contains: |
| The diagrammatic symmetry type of this knot is -. |
| The reverse -K is |
| The 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 | O1O2O3O4U2U4O5O6U5U1U6U3 |
| R3 orbit | {'O1O2O3O4U2U4O5O6U5U1U6U3'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U2U5U4U6O5O6U1U3 |
| Gauss code of K* | O1O2O3O4U2U5U4U6O5O6U1U3 |
| Gauss code of -K* | Same |
| Diagrammatic symmetry type | - |
| Flat genus of the diagram | 3 |
| If K is checkerboard colorable | False |
| If K is almost classical | False |
| Based matrix from Gauss code | [[ 0 -2 -2 2 1 -1 2],[ 2 0 -1 3 1 0 2],[ 2 1 0 2 1 0 0],[-2 -3 -2 0 0 -1 1],[-1 -1 -1 0 0 0 0],[ 1 0 0 1 0 0 1],[-2 -2 0 -1 0 -1 0]] |
| Primitive based matrix | [[ 0 2 2 1 -1 -2 -2],[-2 0 1 0 -1 -2 -3],[-2 -1 0 0 -1 0 -2],[-1 0 0 0 0 -1 -1],[ 1 1 1 0 0 0 0],[ 2 2 0 1 0 0 1],[ 2 3 2 1 0 -1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-2,-1,1,2,2,-1,0,1,2,3,0,1,0,2,0,1,1,0,0,-1] |
| Phi over symmetry | [-2,-2,-1,1,2,2,-1,0,1,2,3,0,1,0,2,0,1,1,0,0,-1] |
| Phi of -K | [-2,-2,-1,1,2,2,-1,1,2,2,4,1,2,1,2,2,2,2,1,1,-1] |
| Phi of K* | [-2,-2,-1,1,2,2,-1,1,2,2,4,1,2,1,2,2,2,2,1,1,-1] |
| Phi of -K* | [-2,-2,-1,1,2,2,-1,0,1,2,3,0,1,0,2,0,1,1,0,0,-1] |
| Symmetry type of based matrix | - |
| u-polynomial | 0 |
| Normalized Jones-Krushkal polynomial | 17z+35 |
| Enhanced Jones-Krushkal polynomial | 17w^2z+35w |
| Inner characteristic polynomial | t^6+23t^4+27t^2+1 |
| Outer characteristic polynomial | t^7+41t^5+53t^3+5t |
| Flat arrow polynomial | -8*K1**2 - 4*K1*K2 + 2*K1 + 4*K2 + 2*K3 + 5 |
| 2-strand cable arrow polynomial | 64*K1**4*K2 - 1344*K1**4 - 896*K1**3*K3 - 1120*K1**2*K2**2 - 128*K1**2*K2*K4 + 5120*K1**2*K2 - 1088*K1**2*K3**2 - 4792*K1**2 + 64*K1*K2*K3**3 - 128*K1*K2*K3*K4 + 5024*K1*K2*K3 - 64*K1*K3**2*K5 + 1312*K1*K3*K4 + 96*K1*K4*K5 - 64*K2**4 - 320*K2**2*K3**2 - 16*K2**2*K4**2 + 448*K2**2*K4 - 3716*K2**2 + 720*K2*K3*K5 + 32*K2*K4*K6 - 192*K3**4 + 256*K3**2*K6 - 2296*K3**2 - 592*K4**2 - 288*K5**2 - 84*K6**2 + 3990 |
| Genus of based matrix | 0 |
| Fillings of based matrix | [[{2, 6}, {4, 5}, {1, 3}]] |
| If K is slice | True |