Min(phi) over symmetries of the knot is: [-3,-1,-1,1,1,3,0,1,1,3,3,0,0,1,1,1,2,3,-1,0,2] |
Flat knots (up to 7 crossings) with same phi are :['6.379'] |
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+63t^5+37t^3+4t |
Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.379'] |
2-strand cable arrow polynomial of the knot is: -256*K1**6 + 1152*K1**4*K2 - 4256*K1**4 + 320*K1**3*K2*K3 + 64*K1**3*K3*K4 - 1568*K1**3*K3 - 1984*K1**2*K2**2 - 640*K1**2*K2*K4 + 7024*K1**2*K2 - 1184*K1**2*K3**2 - 416*K1**2*K4**2 - 3464*K1**2 - 32*K1*K2**2*K3 - 32*K1*K2**2*K5 - 32*K1*K2*K3*K4 + 4944*K1*K2*K3 + 1824*K1*K3*K4 + 336*K1*K4*K5 - 64*K2**4 - 96*K2**2*K3**2 - 48*K2**2*K4**2 + 448*K2**2*K4 - 3132*K2**2 + 128*K2*K3*K5 + 48*K2*K4*K6 - 1736*K3**2 - 664*K4**2 - 96*K5**2 - 12*K6**2 + 3422 |
Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.379'] |
Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.18878', 'vk6.18886', 'vk6.18890', 'vk6.18903', 'vk6.18905', 'vk6.18906', 'vk6.18954', 'vk6.18962', 'vk6.18966', 'vk6.18981', 'vk6.18982', 'vk6.18983', 'vk6.25577', 'vk6.25585', 'vk6.25589', 'vk6.25605', 'vk6.25606', 'vk6.25608', 'vk6.37613', 'vk6.37617', 'vk6.37621', 'vk6.37630', 'vk6.37632', 'vk6.37633', 'vk6.56416', 'vk6.56419', 'vk6.56451', 'vk6.56455', 'vk6.56459', 'vk6.56470', 'vk6.56471', 'vk6.56472'] |
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 | O1O2O3O4O5U4U1O6U3U6U5U2 |
R3 orbit | {'O1O2O3O4O5U4U1O6U3U6U5U2'} |
R3 orbit length | 1 |
Gauss code of -K | O1O2O3O4O5U4U1U6U3O6U5U2 |
Gauss code of K* | O1O2O3O4U5U4U1U6U3O6O5U2 |
Gauss code of -K* | O1O2O3O4U3O5O6U2U6U4U1U5 |
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 -1 -1 3 1],[ 3 0 3 1 0 3 1],[-1 -3 0 -2 -1 2 1],[ 1 -1 2 0 0 3 1],[ 1 0 1 0 0 1 0],[-3 -3 -2 -3 -1 0 0],[-1 -1 -1 -1 0 0 0]] |
Primitive based matrix | [[ 0 3 1 1 -1 -1 -3],[-3 0 0 -2 -1 -3 -3],[-1 0 0 -1 0 -1 -1],[-1 2 1 0 -1 -2 -3],[ 1 1 0 1 0 0 0],[ 1 3 1 2 0 0 -1],[ 3 3 1 3 0 1 0]] |
If based matrix primitive | True |
Phi of primitive based matrix | [-3,-1,-1,1,1,3,0,2,1,3,3,1,0,1,1,1,2,3,0,0,1] |
Phi over symmetry | [-3,-1,-1,1,1,3,0,1,1,3,3,0,0,1,1,1,2,3,-1,0,2] |
Phi of -K | [-3,-1,-1,1,1,3,1,2,1,3,3,0,0,1,1,1,2,3,-1,0,2] |
Phi of K* | [-3,-1,-1,1,1,3,0,2,1,3,3,1,0,1,1,1,2,3,0,1,2] |
Phi of -K* | [-3,-1,-1,1,1,3,0,1,1,3,3,0,0,1,1,1,2,3,-1,0,2] |
Symmetry type of based matrix | c |
u-polynomial | 0 |
Normalized Jones-Krushkal polynomial | 17z+35 |
Enhanced Jones-Krushkal polynomial | 17w^2z+35w |
Inner characteristic polynomial | t^6+41t^4+11t^2 |
Outer characteristic polynomial | t^7+63t^5+37t^3+4t |
Flat arrow polynomial | -8*K1**2 - 4*K1*K2 + 2*K1 + 4*K2 + 2*K3 + 5 |
2-strand cable arrow polynomial | -256*K1**6 + 1152*K1**4*K2 - 4256*K1**4 + 320*K1**3*K2*K3 + 64*K1**3*K3*K4 - 1568*K1**3*K3 - 1984*K1**2*K2**2 - 640*K1**2*K2*K4 + 7024*K1**2*K2 - 1184*K1**2*K3**2 - 416*K1**2*K4**2 - 3464*K1**2 - 32*K1*K2**2*K3 - 32*K1*K2**2*K5 - 32*K1*K2*K3*K4 + 4944*K1*K2*K3 + 1824*K1*K3*K4 + 336*K1*K4*K5 - 64*K2**4 - 96*K2**2*K3**2 - 48*K2**2*K4**2 + 448*K2**2*K4 - 3132*K2**2 + 128*K2*K3*K5 + 48*K2*K4*K6 - 1736*K3**2 - 664*K4**2 - 96*K5**2 - 12*K6**2 + 3422 |
Genus of based matrix | 1 |
Fillings of based matrix | [[{3, 6}, {1, 5}, {2, 4}], [{4, 6}, {1, 5}, {2, 3}]] |
If K is slice | False |