| Min(phi) over symmetries of the knot is: [-3,-1,-1,1,1,3,0,0,1,3,4,0,0,0,1,0,1,1,0,0,2] |
| Flat knots (up to 7 crossings) with same phi are :['6.680'] |
| Arrow polynomial of the knot is: -12*K1**2 - 4*K1*K2 + 2*K1 + 6*K2 + 2*K3 + 7 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.546', '6.591', '6.598', '6.666', '6.680', '6.742', '6.778', '6.805', '6.822', '6.824', '6.1129', '6.1512', '6.1647', '6.1678', '6.1705', '6.1847', '6.1857'] |
| Outer characteristic polynomial of the knot is: t^7+55t^5+54t^3+5t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.680'] |
| 2-strand cable arrow polynomial of the knot is: -384*K1**6 - 256*K1**4*K2**2 + 1376*K1**4*K2 - 3424*K1**4 + 608*K1**3*K2*K3 + 32*K1**3*K3*K4 - 640*K1**3*K3 - 3536*K1**2*K2**2 - 384*K1**2*K2*K4 + 7112*K1**2*K2 - 704*K1**2*K3**2 - 144*K1**2*K4**2 - 3952*K1**2 - 576*K1*K2**2*K3 - 32*K1*K2**2*K5 - 128*K1*K2*K3*K4 + 5192*K1*K2*K3 + 1472*K1*K3*K4 + 304*K1*K4*K5 + 8*K1*K5*K6 - 144*K2**4 - 80*K2**2*K3**2 - 16*K2**2*K4**2 + 736*K2**2*K4 - 3692*K2**2 + 208*K2*K3*K5 + 16*K2*K4*K6 + 8*K3**2*K6 - 1912*K3**2 - 764*K4**2 - 168*K5**2 - 12*K6**2 + 3874 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.680'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.10962', 'vk6.10966', 'vk6.10995', 'vk6.10999', 'vk6.12132', 'vk6.12136', 'vk6.12165', 'vk6.12169', 'vk6.13786', 'vk6.13802', 'vk6.14213', 'vk6.14217', 'vk6.14660', 'vk6.14664', 'vk6.14857', 'vk6.14873', 'vk6.15820', 'vk6.15824', 'vk6.31836', 'vk6.31840', 'vk6.33616', 'vk6.33632', 'vk6.33649', 'vk6.33665', 'vk6.51792', 'vk6.51796', 'vk6.52657', 'vk6.52661', 'vk6.53812', 'vk6.53828', 'vk6.54231', 'vk6.54235'] |
| 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 | O1O2O3O4U3O5U1U5O6U2U6U4 |
| R3 orbit | {'O1O2O3O4U3O5U1U5O6U2U6U4'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U1U5U3O5U6U4O6U2 |
| Gauss code of K* | O1O2O3U4U1U5U3O5U6O4O6U2 |
| Gauss code of -K* | O1O2O3U2O4O5U4O6U1U6U3U5 |
| 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 3 1 1],[ 3 0 2 0 4 1 1],[ 1 -2 0 0 3 0 1],[ 1 0 0 0 1 0 0],[-3 -4 -3 -1 0 0 0],[-1 -1 0 0 0 0 0],[-1 -1 -1 0 0 0 0]] |
| Primitive based matrix | [[ 0 3 1 1 -1 -1 -3],[-3 0 0 0 -1 -3 -4],[-1 0 0 0 0 0 -1],[-1 0 0 0 0 -1 -1],[ 1 1 0 0 0 0 0],[ 1 3 0 1 0 0 -2],[ 3 4 1 1 0 2 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-3,-1,-1,1,1,3,0,0,1,3,4,0,0,0,1,0,1,1,0,0,2] |
| Phi over symmetry | [-3,-1,-1,1,1,3,0,0,1,3,4,0,0,0,1,0,1,1,0,0,2] |
| Phi of -K | [-3,-1,-1,1,1,3,0,2,3,3,2,0,1,2,1,2,2,3,0,2,2] |
| Phi of K* | [-3,-1,-1,1,1,3,2,2,1,3,2,0,1,2,3,2,2,3,0,0,2] |
| Phi of -K* | [-3,-1,-1,1,1,3,0,2,1,1,4,0,0,0,1,0,1,3,0,0,0] |
| 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+33t^4+18t^2+1 |
| Outer characteristic polynomial | t^7+55t^5+54t^3+5t |
| Flat arrow polynomial | -12*K1**2 - 4*K1*K2 + 2*K1 + 6*K2 + 2*K3 + 7 |
| 2-strand cable arrow polynomial | -384*K1**6 - 256*K1**4*K2**2 + 1376*K1**4*K2 - 3424*K1**4 + 608*K1**3*K2*K3 + 32*K1**3*K3*K4 - 640*K1**3*K3 - 3536*K1**2*K2**2 - 384*K1**2*K2*K4 + 7112*K1**2*K2 - 704*K1**2*K3**2 - 144*K1**2*K4**2 - 3952*K1**2 - 576*K1*K2**2*K3 - 32*K1*K2**2*K5 - 128*K1*K2*K3*K4 + 5192*K1*K2*K3 + 1472*K1*K3*K4 + 304*K1*K4*K5 + 8*K1*K5*K6 - 144*K2**4 - 80*K2**2*K3**2 - 16*K2**2*K4**2 + 736*K2**2*K4 - 3692*K2**2 + 208*K2*K3*K5 + 16*K2*K4*K6 + 8*K3**2*K6 - 1912*K3**2 - 764*K4**2 - 168*K5**2 - 12*K6**2 + 3874 |
| Genus of based matrix | 0 |
| Fillings of based matrix | [[{2, 6}, {3, 5}, {1, 4}]] |
| If K is slice | True |