Min(phi) over symmetries of the knot is: [-3,-1,0,1,1,2,0,2,1,4,2,0,0,1,1,0,0,1,0,0,2] |
Flat knots (up to 7 crossings) with same phi are :['6.1277'] |
Arrow polynomial of the knot is: -6*K1**2 - 2*K1*K2 + K1 + 3*K2 + K3 + 4 |
Flat knots (up to 7 crossings) with same arrow polynomial are :['6.323', '6.380', '6.444', '6.472', '6.523', '6.579', '6.592', '6.595', '6.609', '6.614', '6.620', '6.644', '6.648', '6.669', '6.671', '6.681', '6.693', '6.724', '6.725', '6.757', '6.766', '6.785', '6.786', '6.797', '6.798', '6.816', '6.833', '6.972', '6.978', '6.1056', '6.1064', '6.1066', '6.1087', '6.1094', '6.1273', '6.1277', '6.1282', '6.1295', '6.1300', '6.1313', '6.1344', '6.1353', '6.1354'] |
Outer characteristic polynomial of the knot is: t^7+48t^5+55t^3+10t |
Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1277'] |
2-strand cable arrow polynomial of the knot is: -192*K1**6 - 128*K1**4*K2**2 + 1184*K1**4*K2 - 3968*K1**4 + 544*K1**3*K2*K3 + 32*K1**3*K3*K4 - 576*K1**3*K3 + 512*K1**2*K2**3 - 4992*K1**2*K2**2 - 384*K1**2*K2*K4 + 9200*K1**2*K2 - 512*K1**2*K3**2 - 64*K1**2*K3*K5 - 80*K1**2*K4**2 - 5144*K1**2 - 1280*K1*K2**2*K3 - 96*K1*K2*K3*K4 + 6384*K1*K2*K3 + 1504*K1*K3*K4 + 344*K1*K4*K5 + 24*K1*K5*K6 - 440*K2**4 - 48*K2**2*K3**2 - 8*K2**2*K4**2 + 1488*K2**2*K4 - 5062*K2**2 + 392*K2*K3*K5 + 16*K2*K4*K6 - 2344*K3**2 - 1058*K4**2 - 312*K5**2 - 18*K6**2 + 5080 |
Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1277'] |
Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.11267', 'vk6.11347', 'vk6.12532', 'vk6.12645', 'vk6.17623', 'vk6.18915', 'vk6.18993', 'vk6.19342', 'vk6.19637', 'vk6.24080', 'vk6.24174', 'vk6.25509', 'vk6.25612', 'vk6.26114', 'vk6.26534', 'vk6.30949', 'vk6.31074', 'vk6.32129', 'vk6.32250', 'vk6.36420', 'vk6.37652', 'vk6.37701', 'vk6.43518', 'vk6.44775', 'vk6.52017', 'vk6.52110', 'vk6.52935', 'vk6.56482', 'vk6.56658', 'vk6.65400', 'vk6.66110', 'vk6.66149'] |
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 | O1O2O3U1O4O5U4U3O6U2U6U5 |
R3 orbit | {'O1O2O3U1O4O5U4U3O6U2U6U5'} |
R3 orbit length | 1 |
Gauss code of -K | O1O2O3U4U5U2O5U1U6O4O6U3 |
Gauss code of K* | O1O2O3U4U1U5O4U6U3O6O5U2 |
Gauss code of -K* | O1O2O3U2O4O5U1U5O6U4U3U6 |
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 -2 -1 0 -1 3 1],[ 2 0 2 1 0 2 1],[ 1 -2 0 0 0 4 1],[ 0 -1 0 0 0 2 0],[ 1 0 0 0 0 1 0],[-3 -2 -4 -2 -1 0 0],[-1 -1 -1 0 0 0 0]] |
Primitive based matrix | [[ 0 3 1 0 -1 -1 -2],[-3 0 0 -2 -1 -4 -2],[-1 0 0 0 0 -1 -1],[ 0 2 0 0 0 0 -1],[ 1 1 0 0 0 0 0],[ 1 4 1 0 0 0 -2],[ 2 2 1 1 0 2 0]] |
If based matrix primitive | True |
Phi of primitive based matrix | [-3,-1,0,1,1,2,0,2,1,4,2,0,0,1,1,0,0,1,0,0,2] |
Phi over symmetry | [-3,-1,0,1,1,2,0,2,1,4,2,0,0,1,1,0,0,1,0,0,2] |
Phi of -K | [-2,-1,-1,0,1,3,-1,1,1,2,3,0,1,1,0,1,2,3,1,1,2] |
Phi of K* | [-3,-1,0,1,1,2,2,1,0,3,3,1,1,2,2,1,1,1,0,-1,1] |
Phi of -K* | [-2,-1,-1,0,1,3,0,2,1,1,2,0,0,0,1,0,1,4,0,2,0] |
Symmetry type of based matrix | c |
u-polynomial | -t^3+t^2+t |
Normalized Jones-Krushkal polynomial | 2z^2+21z+35 |
Enhanced Jones-Krushkal polynomial | 2w^3z^2-2w^3z+23w^2z+35w |
Inner characteristic polynomial | t^6+32t^4+20t^2+1 |
Outer characteristic polynomial | t^7+48t^5+55t^3+10t |
Flat arrow polynomial | -6*K1**2 - 2*K1*K2 + K1 + 3*K2 + K3 + 4 |
2-strand cable arrow polynomial | -192*K1**6 - 128*K1**4*K2**2 + 1184*K1**4*K2 - 3968*K1**4 + 544*K1**3*K2*K3 + 32*K1**3*K3*K4 - 576*K1**3*K3 + 512*K1**2*K2**3 - 4992*K1**2*K2**2 - 384*K1**2*K2*K4 + 9200*K1**2*K2 - 512*K1**2*K3**2 - 64*K1**2*K3*K5 - 80*K1**2*K4**2 - 5144*K1**2 - 1280*K1*K2**2*K3 - 96*K1*K2*K3*K4 + 6384*K1*K2*K3 + 1504*K1*K3*K4 + 344*K1*K4*K5 + 24*K1*K5*K6 - 440*K2**4 - 48*K2**2*K3**2 - 8*K2**2*K4**2 + 1488*K2**2*K4 - 5062*K2**2 + 392*K2*K3*K5 + 16*K2*K4*K6 - 2344*K3**2 - 1058*K4**2 - 312*K5**2 - 18*K6**2 + 5080 |
Genus of based matrix | 1 |
Fillings of based matrix | [[{1, 6}, {4, 5}, {2, 3}]] |
If K is slice | False |