| Min(phi) over symmetries of the knot is: [-2,-1,0,1,1,1,0,0,2,2,2,1,1,1,1,-1,0,1,0,1,1] |
| Flat knots (up to 7 crossings) with same phi are :['6.1921'] |
| Arrow polynomial of the knot is: 4*K1**3 - 2*K1**2 - 8*K1*K2 + K1 + K2 + 3*K3 + 2 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.1030', '6.1062', '6.1226', '6.1508', '6.1525', '6.1596', '6.1724', '6.1729', '6.1735', '6.1738', '6.1789', '6.1809', '6.1921'] |
| Outer characteristic polynomial of the knot is: t^7+26t^5+49t^3+14t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1921'] |
| 2-strand cable arrow polynomial of the knot is: 192*K1**4*K2 - 928*K1**4 + 128*K1**3*K2*K3 - 64*K1**3*K3 + 352*K1**2*K2**3 + 128*K1**2*K2**2*K4 - 4304*K1**2*K2**2 + 64*K1**2*K2*K3**2 - 288*K1**2*K2*K4 + 5360*K1**2*K2 - 512*K1**2*K3**2 - 32*K1**2*K4**2 - 4084*K1**2 + 512*K1*K2**3*K3 - 1408*K1*K2**2*K3 - 704*K1*K2**2*K5 - 384*K1*K2*K3*K4 + 6696*K1*K2*K3 + 1184*K1*K3*K4 + 264*K1*K4*K5 - 32*K2**6 + 224*K2**4*K4 - 1400*K2**4 - 96*K2**3*K6 - 704*K2**2*K3**2 - 128*K2**2*K4**2 + 2272*K2**2*K4 - 3890*K2**2 + 1144*K2*K3*K5 + 72*K2*K4*K6 - 2276*K3**2 - 842*K4**2 - 336*K5**2 - 6*K6**2 + 3824 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1921'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.10149', 'vk6.10218', 'vk6.10361', 'vk6.10436', 'vk6.16693', 'vk6.19073', 'vk6.19120', 'vk6.19251', 'vk6.19546', 'vk6.23011', 'vk6.23128', 'vk6.25702', 'vk6.25749', 'vk6.26065', 'vk6.26444', 'vk6.29936', 'vk6.29999', 'vk6.30093', 'vk6.35000', 'vk6.35127', 'vk6.37796', 'vk6.37856', 'vk6.42573', 'vk6.44654', 'vk6.51633', 'vk6.51736', 'vk6.54906', 'vk6.56590', 'vk6.59332', 'vk6.64876', 'vk6.66182', 'vk6.66213'] |
| 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 | O1O2O3U1U4U2O4O5O6U3U6U5 |
| R3 orbit | {'O1O2O3U1U4U2O4O5O6U3U6U5'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U4U3U5O6O4O5U2U1U6 |
| Gauss code of K* | O1O2O3U2U4U5O6O5O4U1U3U6 |
| Gauss code of -K* | O1O2O3U2U1U4O5O4O6U3U5U6 |
| 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 1 1],[ 2 0 1 2 1 1 1],[-1 -1 0 0 -1 1 1],[ 0 -2 0 0 0 2 1],[ 1 -1 1 0 0 1 1],[-1 -1 -1 -2 -1 0 0],[-1 -1 -1 -1 -1 0 0]] |
| Primitive based matrix | [[ 0 1 1 1 0 -1 -2],[-1 0 1 1 0 -1 -1],[-1 -1 0 0 -1 -1 -1],[-1 -1 0 0 -2 -1 -1],[ 0 0 1 2 0 0 -2],[ 1 1 1 1 0 0 -1],[ 2 1 1 1 2 1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-1,-1,-1,0,1,2,-1,-1,0,1,1,0,1,1,1,2,1,1,0,2,1] |
| Phi over symmetry | [-2,-1,0,1,1,1,0,0,2,2,2,1,1,1,1,-1,0,1,0,1,1] |
| Phi of -K | [-2,-1,0,1,1,1,0,0,2,2,2,1,1,1,1,-1,0,1,0,1,1] |
| Phi of K* | [-1,-1,-1,0,1,2,-1,0,-1,1,2,1,1,1,2,0,1,2,1,0,0] |
| Phi of -K* | [-2,-1,0,1,1,1,1,2,1,1,1,0,1,1,1,0,1,2,1,1,0] |
| Symmetry type of based matrix | c |
| u-polynomial | t^2-2t |
| Normalized Jones-Krushkal polynomial | 7z^2+28z+29 |
| Enhanced Jones-Krushkal polynomial | 7w^3z^2+28w^2z+29w |
| Inner characteristic polynomial | t^6+18t^4+16t^2+1 |
| Outer characteristic polynomial | t^7+26t^5+49t^3+14t |
| Flat arrow polynomial | 4*K1**3 - 2*K1**2 - 8*K1*K2 + K1 + K2 + 3*K3 + 2 |
| 2-strand cable arrow polynomial | 192*K1**4*K2 - 928*K1**4 + 128*K1**3*K2*K3 - 64*K1**3*K3 + 352*K1**2*K2**3 + 128*K1**2*K2**2*K4 - 4304*K1**2*K2**2 + 64*K1**2*K2*K3**2 - 288*K1**2*K2*K4 + 5360*K1**2*K2 - 512*K1**2*K3**2 - 32*K1**2*K4**2 - 4084*K1**2 + 512*K1*K2**3*K3 - 1408*K1*K2**2*K3 - 704*K1*K2**2*K5 - 384*K1*K2*K3*K4 + 6696*K1*K2*K3 + 1184*K1*K3*K4 + 264*K1*K4*K5 - 32*K2**6 + 224*K2**4*K4 - 1400*K2**4 - 96*K2**3*K6 - 704*K2**2*K3**2 - 128*K2**2*K4**2 + 2272*K2**2*K4 - 3890*K2**2 + 1144*K2*K3*K5 + 72*K2*K4*K6 - 2276*K3**2 - 842*K4**2 - 336*K5**2 - 6*K6**2 + 3824 |
| Genus of based matrix | 2 |
| Fillings of based matrix | [[{1, 6}, {2, 5}, {3, 4}], [{1, 6}, {2, 5}, {4}, {3}], [{1, 6}, {3, 5}, {2, 4}], [{1, 6}, {3, 5}, {4}, {2}], [{1, 6}, {4, 5}, {2, 3}], [{1, 6}, {4, 5}, {3}, {2}], [{1, 6}, {5}, {2, 4}, {3}], [{1, 6}, {5}, {3, 4}, {2}], [{1, 6}, {5}, {4}, {2, 3}], [{2, 6}, {1, 5}, {3, 4}], [{2, 6}, {1, 5}, {4}, {3}], [{2, 6}, {3, 5}, {1, 4}], [{2, 6}, {3, 5}, {4}, {1}], [{2, 6}, {4, 5}, {1, 3}], [{2, 6}, {4, 5}, {3}, {1}], [{2, 6}, {5}, {1, 4}, {3}], [{2, 6}, {5}, {3, 4}, {1}], [{2, 6}, {5}, {4}, {1, 3}], [{3, 6}, {1, 5}, {2, 4}], [{3, 6}, {1, 5}, {4}, {2}], [{3, 6}, {2, 5}, {1, 4}], [{3, 6}, {2, 5}, {4}, {1}], [{3, 6}, {4, 5}, {1, 2}], [{3, 6}, {4, 5}, {2}, {1}], [{3, 6}, {5}, {1, 4}, {2}], [{3, 6}, {5}, {2, 4}, {1}], [{3, 6}, {5}, {4}, {1, 2}], [{4, 6}, {1, 5}, {2, 3}], [{4, 6}, {1, 5}, {3}, {2}], [{4, 6}, {2, 5}, {1, 3}], [{4, 6}, {2, 5}, {3}, {1}], [{4, 6}, {3, 5}, {1, 2}], [{4, 6}, {3, 5}, {2}, {1}], [{4, 6}, {5}, {1, 3}, {2}], [{4, 6}, {5}, {2, 3}, {1}], [{4, 6}, {5}, {3}, {1, 2}], [{4, 6}, {5}, {3}, {2}, {1}], [{5, 6}, {1, 4}, {2, 3}], [{5, 6}, {1, 4}, {3}, {2}], [{5, 6}, {2, 4}, {1, 3}], [{5, 6}, {2, 4}, {3}, {1}], [{5, 6}, {3, 4}, {1, 2}], [{5, 6}, {3, 4}, {2}, {1}], [{5, 6}, {4}, {1, 3}, {2}], [{5, 6}, {4}, {2, 3}, {1}], [{5, 6}, {4}, {3}, {1, 2}], [{6}, {1, 5}, {2, 4}, {3}], [{6}, {1, 5}, {3, 4}, {2}], [{6}, {1, 5}, {4}, {2, 3}], [{6}, {2, 5}, {1, 4}, {3}], [{6}, {2, 5}, {3, 4}, {1}], [{6}, {2, 5}, {4}, {1, 3}], [{6}, {3, 5}, {1, 4}, {2}], [{6}, {3, 5}, {2, 4}, {1}], [{6}, {3, 5}, {4}, {1, 2}], [{6}, {4, 5}, {1, 3}, {2}], [{6}, {4, 5}, {2, 3}, {1}], [{6}, {4, 5}, {3}, {1, 2}], [{6}, {5}, {1, 4}, {2, 3}], [{6}, {5}, {2, 4}, {1, 3}], [{6}, {5}, {3, 4}, {1, 2}], [{6}, {5}, {4}, {2, 3}, {1}]] |
| If K is slice | False |