| Min(phi) over symmetries of the knot is: [-3,-1,0,1,1,2,1,0,1,3,3,0,1,2,2,0,1,0,-1,0,1] |
| Flat knots (up to 7 crossings) with same phi are :['6.1344'] |
| 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+50t^5+61t^3+5t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1344'] |
| 2-strand cable arrow polynomial of the knot is: -192*K1**4*K2**2 + 512*K1**4*K2 - 2480*K1**4 + 448*K1**3*K2*K3 + 32*K1**3*K3*K4 - 992*K1**3*K3 + 448*K1**2*K2**3 - 2736*K1**2*K2**2 - 640*K1**2*K2*K4 + 5696*K1**2*K2 - 528*K1**2*K3**2 - 160*K1**2*K3*K5 - 32*K1**2*K4**2 - 3180*K1**2 - 96*K1*K2**2*K3 - 64*K1*K2*K3*K4 + 4056*K1*K2*K3 + 976*K1*K3*K4 + 200*K1*K4*K5 - 264*K2**4 - 32*K2**2*K3**2 - 8*K2**2*K4**2 + 488*K2**2*K4 - 2534*K2**2 + 272*K2*K3*K5 + 16*K2*K4*K6 + 24*K3**2*K6 - 1364*K3**2 - 454*K4**2 - 168*K5**2 - 18*K6**2 + 2772 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1344'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.13941', 'vk6.13953', 'vk6.14037', 'vk6.14049', 'vk6.15008', 'vk6.15020', 'vk6.15130', 'vk6.15142', 'vk6.17445', 'vk6.17464', 'vk6.17484', 'vk6.23953', 'vk6.23973', 'vk6.23984', 'vk6.24004', 'vk6.33751', 'vk6.33823', 'vk6.33841', 'vk6.34294', 'vk6.36254', 'vk6.36264', 'vk6.43414', 'vk6.53877', 'vk6.53885', 'vk6.53917', 'vk6.54423', 'vk6.55595', 'vk6.55611', 'vk6.60084', 'vk6.60098', 'vk6.60118', 'vk6.65313'] |
| 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 | O1O2O3U1O4O5U4U6U3O6U2U5 |
| R3 orbit | {'O1O2O3U1O4O5U4U6U3O6U2U5'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U4U2O5U1U5U6O4O6U3 |
| Gauss code of K* | O1O2O3U2O4O5U6U4U3O6U1U5 |
| Gauss code of -K* | O1O2O3U4U3O5U1U6U5O4O6U2 |
| 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 0 1 -1 3 -1],[ 2 0 2 1 0 2 1],[ 0 -2 0 1 0 3 -1],[-1 -1 -1 0 0 1 -1],[ 1 0 0 0 0 1 1],[-3 -2 -3 -1 -1 0 -3],[ 1 -1 1 1 -1 3 0]] |
| Primitive based matrix | [[ 0 3 1 0 -1 -1 -2],[-3 0 -1 -3 -1 -3 -2],[-1 1 0 -1 0 -1 -1],[ 0 3 1 0 0 -1 -2],[ 1 1 0 0 0 1 0],[ 1 3 1 1 -1 0 -1],[ 2 2 1 2 0 1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-3,-1,0,1,1,2,1,3,1,3,2,1,0,1,1,0,1,2,-1,0,1] |
| Phi over symmetry | [-3,-1,0,1,1,2,1,0,1,3,3,0,1,2,2,0,1,0,-1,0,1] |
| Phi of -K | [-2,-1,-1,0,1,3,0,1,0,2,3,1,0,1,1,1,2,3,0,0,1] |
| Phi of K* | [-3,-1,0,1,1,2,1,0,1,3,3,0,1,2,2,0,1,0,-1,0,1] |
| Phi of -K* | [-2,-1,-1,0,1,3,0,1,2,1,2,1,0,0,1,1,1,3,1,3,1] |
| Symmetry type of based matrix | c |
| u-polynomial | -t^3+t^2+t |
| Normalized Jones-Krushkal polynomial | 2z^2+19z+31 |
| Enhanced Jones-Krushkal polynomial | 2w^3z^2+19w^2z+31w |
| Inner characteristic polynomial | t^6+34t^4+36t^2+1 |
| Outer characteristic polynomial | t^7+50t^5+61t^3+5t |
| Flat arrow polynomial | -6*K1**2 - 2*K1*K2 + K1 + 3*K2 + K3 + 4 |
| 2-strand cable arrow polynomial | -192*K1**4*K2**2 + 512*K1**4*K2 - 2480*K1**4 + 448*K1**3*K2*K3 + 32*K1**3*K3*K4 - 992*K1**3*K3 + 448*K1**2*K2**3 - 2736*K1**2*K2**2 - 640*K1**2*K2*K4 + 5696*K1**2*K2 - 528*K1**2*K3**2 - 160*K1**2*K3*K5 - 32*K1**2*K4**2 - 3180*K1**2 - 96*K1*K2**2*K3 - 64*K1*K2*K3*K4 + 4056*K1*K2*K3 + 976*K1*K3*K4 + 200*K1*K4*K5 - 264*K2**4 - 32*K2**2*K3**2 - 8*K2**2*K4**2 + 488*K2**2*K4 - 2534*K2**2 + 272*K2*K3*K5 + 16*K2*K4*K6 + 24*K3**2*K6 - 1364*K3**2 - 454*K4**2 - 168*K5**2 - 18*K6**2 + 2772 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {2, 5}, {3, 4}], [{1, 6}, {3, 5}, {2, 4}], [{2, 6}, {1, 5}, {3, 4}], [{2, 6}, {4, 5}, {1, 3}], [{5, 6}, {3, 4}, {1, 2}]] |
| If K is slice | False |