| Min(phi) over symmetries of the knot is: [-3,-2,0,1,2,2,0,2,3,2,3,1,2,1,1,0,1,1,2,2,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.523'] |
| 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+63t^5+60t^3+4t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.523'] |
| 2-strand cable arrow polynomial of the knot is: -64*K1**6 + 64*K1**4*K2 - 1360*K1**4 + 32*K1**3*K2*K3 - 192*K1**3*K3 - 1488*K1**2*K2**2 + 96*K1**2*K2*K3**2 - 192*K1**2*K2*K4 + 3760*K1**2*K2 - 496*K1**2*K3**2 - 96*K1**2*K3*K5 - 48*K1**2*K4**2 - 2464*K1**2 - 448*K1*K2**2*K3 + 3136*K1*K2*K3 + 904*K1*K3*K4 + 40*K1*K4*K5 - 88*K2**4 - 160*K2**2*K3**2 - 8*K2**2*K4**2 + 344*K2**2*K4 - 2070*K2**2 + 144*K2*K3*K5 + 8*K2*K4*K6 - 1140*K3**2 - 294*K4**2 - 28*K5**2 - 2*K6**2 + 2108 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.523'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.16552', 'vk6.16643', 'vk6.18148', 'vk6.18484', 'vk6.22955', 'vk6.23074', 'vk6.24607', 'vk6.25020', 'vk6.34952', 'vk6.35071', 'vk6.35375', 'vk6.35794', 'vk6.36746', 'vk6.37165', 'vk6.39407', 'vk6.41600', 'vk6.42525', 'vk6.42634', 'vk6.42852', 'vk6.43129', 'vk6.44018', 'vk6.44330', 'vk6.45987', 'vk6.47663', 'vk6.54799', 'vk6.55349', 'vk6.56246', 'vk6.57429', 'vk6.59231', 'vk6.59790', 'vk6.60850', 'vk6.62100', 'vk6.64781', 'vk6.64844', 'vk6.65611', 'vk6.65918', 'vk6.68083', 'vk6.68146', 'vk6.68686', 'vk6.68897'] |
| 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 | O1O2O3O4O5U2U4U1O6U5U6U3 |
| R3 orbit | {'O1O2O3O4O5U2U4U1O6U5U6U3', 'O1O2O3O4U1U5U2O6U4U6O5U3'} |
| R3 orbit length | 2 |
| Gauss code of -K | O1O2O3O4O5U3U6U1O6U5U2U4 |
| Gauss code of K* | O1O2O3U4O5O4O6U3U1U6U2U5 |
| Gauss code of -K* | O1O2O3U2O4O5O6U3U5U1U6U4 |
| 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 -3 2 0 2 1],[ 2 0 -1 3 1 3 1],[ 3 1 0 3 1 2 1],[-2 -3 -3 0 -1 0 1],[ 0 -1 -1 1 0 1 1],[-2 -3 -2 0 -1 0 1],[-1 -1 -1 -1 -1 -1 0]] |
| Primitive based matrix | [[ 0 2 2 1 0 -2 -3],[-2 0 0 1 -1 -3 -2],[-2 0 0 1 -1 -3 -3],[-1 -1 -1 0 -1 -1 -1],[ 0 1 1 1 0 -1 -1],[ 2 3 3 1 1 0 -1],[ 3 2 3 1 1 1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-2,-1,0,2,3,0,-1,1,3,2,-1,1,3,3,1,1,1,1,1,1] |
| Phi over symmetry | [-3,-2,0,1,2,2,0,2,3,2,3,1,2,1,1,0,1,1,2,2,0] |
| Phi of -K | [-3,-2,0,1,2,2,0,2,3,2,3,1,2,1,1,0,1,1,2,2,0] |
| Phi of K* | [-2,-2,-1,0,2,3,0,2,1,1,2,2,1,1,3,0,2,3,1,2,0] |
| Phi of -K* | [-3,-2,0,1,2,2,1,1,1,2,3,1,1,3,3,1,1,1,-1,-1,0] |
| Symmetry type of based matrix | c |
| u-polynomial | t^3-t^2-t |
| Normalized Jones-Krushkal polynomial | 13z+27 |
| Enhanced Jones-Krushkal polynomial | 13w^2z+27w |
| Inner characteristic polynomial | t^6+41t^4+21t^2+1 |
| Outer characteristic polynomial | t^7+63t^5+60t^3+4t |
| Flat arrow polynomial | -6*K1**2 - 2*K1*K2 + K1 + 3*K2 + K3 + 4 |
| 2-strand cable arrow polynomial | -64*K1**6 + 64*K1**4*K2 - 1360*K1**4 + 32*K1**3*K2*K3 - 192*K1**3*K3 - 1488*K1**2*K2**2 + 96*K1**2*K2*K3**2 - 192*K1**2*K2*K4 + 3760*K1**2*K2 - 496*K1**2*K3**2 - 96*K1**2*K3*K5 - 48*K1**2*K4**2 - 2464*K1**2 - 448*K1*K2**2*K3 + 3136*K1*K2*K3 + 904*K1*K3*K4 + 40*K1*K4*K5 - 88*K2**4 - 160*K2**2*K3**2 - 8*K2**2*K4**2 + 344*K2**2*K4 - 2070*K2**2 + 144*K2*K3*K5 + 8*K2*K4*K6 - 1140*K3**2 - 294*K4**2 - 28*K5**2 - 2*K6**2 + 2108 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {4, 5}, {2, 3}]] |
| If K is slice | False |