Min(phi) over symmetries of the knot is: [-3,-2,-2,2,2,3,0,1,1,4,3,1,0,2,1,2,4,4,-1,0,1] |
Flat knots (up to 7 crossings) with same phi are :['6.823'] |
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+105t^5+175t^3+7t |
Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.823'] |
2-strand cable arrow polynomial of the knot is: 128*K1**4*K2 - 1920*K1**4 - 2624*K1**2*K2**2 + 8096*K1**2*K2 - 64*K1**2*K3**2 - 6880*K1**2 + 256*K1*K2**3*K3 - 1536*K1*K2**2*K3 - 512*K1*K2*K3*K4 + 6464*K1*K2*K3 + 1408*K1*K3*K4 + 128*K1*K4*K5 - 416*K2**4 - 512*K2**2*K3**2 - 48*K2**2*K4**2 + 2032*K2**2*K4 - 6276*K2**2 + 576*K2*K3*K5 + 48*K2*K4*K6 - 2880*K3**2 - 1184*K4**2 - 128*K5**2 - 12*K6**2 + 5854 |
Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.823'] |
Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.72435', 'vk6.72497', 'vk6.72856', 'vk6.72909', 'vk6.74452', 'vk6.75065', 'vk6.76960', 'vk6.77792', 'vk6.77978', 'vk6.79460', 'vk6.79908', 'vk6.80929', 'vk6.87240', 'vk6.89370'] |
The R3 orbit of minmal crossing diagrams contains: |
The diagrammatic symmetry type of this knot is a. |
The fillings (up to the first 10) associated to the algebraic genus: |
Or click here to check the fillings |
invariant | value |
---|---|
Gauss code | O1O2O3O4U2O5U1U6U5U4O6U3 |
R3 orbit | {'O1O2O3O4U2O5U1U6U5U4O6U3'} |
R3 orbit length | 1 |
Gauss code of -K | Same |
Gauss code of K* | Same |
Gauss code of -K* | Same |
Diagrammatic symmetry type | a |
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 2 3 2 -2],[ 3 0 0 4 3 1 1],[ 2 0 0 2 1 0 1],[-2 -4 -2 0 1 1 -4],[-3 -3 -1 -1 0 0 -4],[-2 -1 0 -1 0 0 -2],[ 2 -1 -1 4 4 2 0]] |
Primitive based matrix | [[ 0 3 2 2 -2 -2 -3],[-3 0 0 -1 -1 -4 -3],[-2 0 0 -1 0 -2 -1],[-2 1 1 0 -2 -4 -4],[ 2 1 0 2 0 1 0],[ 2 4 2 4 -1 0 -1],[ 3 3 1 4 0 1 0]] |
If based matrix primitive | True |
Phi of primitive based matrix | [-3,-2,-2,2,2,3,0,1,1,4,3,1,0,2,1,2,4,4,-1,0,1] |
Phi over symmetry | [-3,-2,-2,2,2,3,0,1,1,4,3,1,0,2,1,2,4,4,-1,0,1] |
Phi of -K | [-3,-2,-2,2,2,3,0,1,1,4,3,1,0,2,1,2,4,4,-1,0,1] |
Phi of K* | [-3,-2,-2,2,2,3,0,1,1,4,3,1,0,2,1,2,4,4,-1,0,1] |
Phi of -K* | [-3,-2,-2,2,2,3,0,1,1,4,3,1,0,2,1,2,4,4,-1,0,1] |
Symmetry type of based matrix | a |
u-polynomial | 0 |
Normalized Jones-Krushkal polynomial | 2z^2+22z+37 |
Enhanced Jones-Krushkal polynomial | 2w^3z^2+22w^2z+37w |
Inner characteristic polynomial | t^6+71t^4+71t^2+1 |
Outer characteristic polynomial | t^7+105t^5+175t^3+7t |
Flat arrow polynomial | -8*K1**2 - 4*K1*K2 + 2*K1 + 4*K2 + 2*K3 + 5 |
2-strand cable arrow polynomial | 128*K1**4*K2 - 1920*K1**4 - 2624*K1**2*K2**2 + 8096*K1**2*K2 - 64*K1**2*K3**2 - 6880*K1**2 + 256*K1*K2**3*K3 - 1536*K1*K2**2*K3 - 512*K1*K2*K3*K4 + 6464*K1*K2*K3 + 1408*K1*K3*K4 + 128*K1*K4*K5 - 416*K2**4 - 512*K2**2*K3**2 - 48*K2**2*K4**2 + 2032*K2**2*K4 - 6276*K2**2 + 576*K2*K3*K5 + 48*K2*K4*K6 - 2880*K3**2 - 1184*K4**2 - 128*K5**2 - 12*K6**2 + 5854 |
Genus of based matrix | 0 |
Fillings of based matrix | [[{3, 6}, {2, 5}, {1, 4}]] |
If K is slice | True |