| Min(phi) over symmetries of the knot is: [-3,-2,0,1,2,2,0,2,1,2,3,2,1,1,2,1,0,1,0,0,-1] |
| Flat knots (up to 7 crossings) with same phi are :['6.669'] |
| 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+71t^5+129t^3+6t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.669'] |
| 2-strand cable arrow polynomial of the knot is: 160*K1**4*K2 - 1952*K1**4 - 800*K1**3*K3 + 192*K1**2*K2**3 - 2304*K1**2*K2**2 - 224*K1**2*K2*K4 + 6672*K1**2*K2 - 512*K1**2*K3**2 - 5056*K1**2 - 64*K1*K2*K3*K4 + 4648*K1*K2*K3 + 912*K1*K3*K4 + 48*K1*K4*K5 - 296*K2**4 - 96*K2**2*K3**2 - 8*K2**2*K4**2 + 584*K2**2*K4 - 3742*K2**2 + 352*K2*K3*K5 + 16*K2*K4*K6 + 24*K3**2*K6 - 1840*K3**2 - 526*K4**2 - 160*K5**2 - 18*K6**2 + 3988 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.669'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.16511', 'vk6.16604', 'vk6.18077', 'vk6.18413', 'vk6.22942', 'vk6.23039', 'vk6.24528', 'vk6.24945', 'vk6.34911', 'vk6.35020', 'vk6.36667', 'vk6.37089', 'vk6.42480', 'vk6.42593', 'vk6.43947', 'vk6.44262', 'vk6.54754', 'vk6.54851', 'vk6.55906', 'vk6.56193', 'vk6.59218', 'vk6.59283', 'vk6.60435', 'vk6.60792', 'vk6.64762', 'vk6.64825', 'vk6.65551', 'vk6.65861', 'vk6.68062', 'vk6.68127', 'vk6.68633', 'vk6.68846'] |
| 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 | O1O2O3O4U2O5U6U3O6U1U4U5 |
| R3 orbit | {'O1O2O3O4U2O5U6U3O6U1U4U5'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U5U1U4O6U2U6O5U3 |
| Gauss code of K* | O1O2O3U1U4U5U2O4U3O6O5U6 |
| Gauss code of -K* | O1O2O3U4O5O4U1O6U2U5U6U3 |
| 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 -2 0 2 3 -1],[ 2 0 -1 2 3 3 1],[ 2 1 0 1 2 2 1],[ 0 -2 -1 0 0 1 0],[-2 -3 -2 0 0 1 -2],[-3 -3 -2 -1 -1 0 -3],[ 1 -1 -1 0 2 3 0]] |
| Primitive based matrix | [[ 0 3 2 0 -1 -2 -2],[-3 0 -1 -1 -3 -2 -3],[-2 1 0 0 -2 -2 -3],[ 0 1 0 0 0 -1 -2],[ 1 3 2 0 0 -1 -1],[ 2 2 2 1 1 0 1],[ 2 3 3 2 1 -1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-3,-2,0,1,2,2,1,1,3,2,3,0,2,2,3,0,1,2,1,1,-1] |
| Phi over symmetry | [-3,-2,0,1,2,2,0,2,1,2,3,2,1,1,2,1,0,1,0,0,-1] |
| Phi of -K | [-2,-2,-1,0,2,3,-1,0,1,2,3,0,0,1,2,1,1,1,2,2,0] |
| Phi of K* | [-3,-2,0,1,2,2,0,2,1,2,3,2,1,1,2,1,0,1,0,0,-1] |
| Phi of -K* | [-2,-2,-1,0,2,3,-1,1,2,3,3,1,1,2,2,0,2,3,0,1,1] |
| Symmetry type of based matrix | c |
| u-polynomial | -t^3+t^2+t |
| Normalized Jones-Krushkal polynomial | 3z^2+22z+33 |
| Enhanced Jones-Krushkal polynomial | 3w^3z^2+22w^2z+33w |
| Inner characteristic polynomial | t^6+49t^4+72t^2+1 |
| Outer characteristic polynomial | t^7+71t^5+129t^3+6t |
| Flat arrow polynomial | -6*K1**2 - 2*K1*K2 + K1 + 3*K2 + K3 + 4 |
| 2-strand cable arrow polynomial | 160*K1**4*K2 - 1952*K1**4 - 800*K1**3*K3 + 192*K1**2*K2**3 - 2304*K1**2*K2**2 - 224*K1**2*K2*K4 + 6672*K1**2*K2 - 512*K1**2*K3**2 - 5056*K1**2 - 64*K1*K2*K3*K4 + 4648*K1*K2*K3 + 912*K1*K3*K4 + 48*K1*K4*K5 - 296*K2**4 - 96*K2**2*K3**2 - 8*K2**2*K4**2 + 584*K2**2*K4 - 3742*K2**2 + 352*K2*K3*K5 + 16*K2*K4*K6 + 24*K3**2*K6 - 1840*K3**2 - 526*K4**2 - 160*K5**2 - 18*K6**2 + 3988 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{4, 6}, {2, 5}, {1, 3}]] |
| If K is slice | False |