| Min(phi) over symmetries of the knot is: [-3,-2,1,1,1,2,0,1,2,3,4,1,1,2,2,0,-1,0,-1,1,1] |
| Flat knots (up to 7 crossings) with same phi are :['6.903'] |
| Arrow polynomial of the knot is: 4*K1**3 - 4*K1**2 - 6*K1*K2 + 2*K2 + 2*K3 + 3 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.552', '6.652', '6.764', '6.776', '6.784', '6.839', '6.903', '6.1010', '6.1166'] |
| Outer characteristic polynomial of the knot is: t^7+64t^5+97t^3+9t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.903'] |
| 2-strand cable arrow polynomial of the knot is: -96*K1**4 - 64*K1**3*K3 - 192*K1**2*K2**4 + 192*K1**2*K2**3 + 128*K1**2*K2**2*K4 - 4528*K1**2*K2**2 - 544*K1**2*K2*K4 + 6208*K1**2*K2 - 32*K1**2*K3**2 - 160*K1**2*K4**2 - 5360*K1**2 + 480*K1*K2**3*K3 + 224*K1*K2**2*K3*K4 - 1184*K1*K2**2*K3 - 352*K1*K2**2*K5 - 224*K1*K2*K3*K4 - 64*K1*K2*K3*K6 + 6344*K1*K2*K3 + 1240*K1*K3*K4 + 176*K1*K4*K5 - 32*K2**6 + 128*K2**4*K4 - 688*K2**4 - 32*K2**3*K6 - 624*K2**2*K3**2 - 568*K2**2*K4**2 + 2376*K2**2*K4 - 4564*K2**2 + 512*K2*K3*K5 + 296*K2*K4*K6 + 8*K3**2*K6 - 2008*K3**2 - 1084*K4**2 - 80*K5**2 - 28*K6**2 + 4194 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.903'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.11071', 'vk6.11149', 'vk6.12235', 'vk6.12342', 'vk6.18327', 'vk6.18666', 'vk6.24763', 'vk6.25222', 'vk6.30652', 'vk6.30745', 'vk6.31882', 'vk6.31951', 'vk6.36949', 'vk6.37413', 'vk6.44142', 'vk6.44465', 'vk6.51870', 'vk6.51917', 'vk6.52737', 'vk6.52848', 'vk6.56105', 'vk6.56326', 'vk6.60622', 'vk6.60955', 'vk6.63533', 'vk6.63578', 'vk6.64013', 'vk6.64058', 'vk6.65753', 'vk6.66019', 'vk6.68763', 'vk6.68973'] |
| 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 | O1O2O3O4U2U5O6O5U1U4U6U3 |
| R3 orbit | {'O1O2O3O4U2U5O6O5U1U4U6U3'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U2U5U1U4O6O5U6U3 |
| Gauss code of K* | O1O2O3O4U1U5U4U2O5O6U3U6 |
| Gauss code of -K* | O1O2O3O4U5U2O5O6U3U1U6U4 |
| 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 -2 2 1 1 1],[ 3 0 0 4 2 3 1],[ 2 0 0 2 1 2 1],[-2 -4 -2 0 -1 -1 0],[-1 -2 -1 1 0 -1 0],[-1 -3 -2 1 1 0 1],[-1 -1 -1 0 0 -1 0]] |
| Primitive based matrix | [[ 0 2 1 1 1 -2 -3],[-2 0 0 -1 -1 -2 -4],[-1 0 0 0 -1 -1 -1],[-1 1 0 0 -1 -1 -2],[-1 1 1 1 0 -2 -3],[ 2 2 1 1 2 0 0],[ 3 4 1 2 3 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,-1,-1,2,3,0,1,1,2,4,0,1,1,1,1,1,2,2,3,0] |
| Phi over symmetry | [-3,-2,1,1,1,2,0,1,2,3,4,1,1,2,2,0,-1,0,-1,1,1] |
| Phi of -K | [-3,-2,1,1,1,2,1,1,2,3,1,1,2,2,2,-1,-1,0,0,0,1] |
| Phi of K* | [-2,-1,-1,-1,2,3,0,0,1,2,1,-1,0,2,2,1,1,1,2,3,1] |
| Phi of -K* | [-3,-2,1,1,1,2,0,1,2,3,4,1,1,2,2,0,-1,0,-1,1,1] |
| Symmetry type of based matrix | c |
| u-polynomial | t^3-3t |
| Normalized Jones-Krushkal polynomial | 7z^2+26z+25 |
| Enhanced Jones-Krushkal polynomial | 7w^3z^2+26w^2z+25w |
| Inner characteristic polynomial | t^6+44t^4+59t^2+4 |
| Outer characteristic polynomial | t^7+64t^5+97t^3+9t |
| Flat arrow polynomial | 4*K1**3 - 4*K1**2 - 6*K1*K2 + 2*K2 + 2*K3 + 3 |
| 2-strand cable arrow polynomial | -96*K1**4 - 64*K1**3*K3 - 192*K1**2*K2**4 + 192*K1**2*K2**3 + 128*K1**2*K2**2*K4 - 4528*K1**2*K2**2 - 544*K1**2*K2*K4 + 6208*K1**2*K2 - 32*K1**2*K3**2 - 160*K1**2*K4**2 - 5360*K1**2 + 480*K1*K2**3*K3 + 224*K1*K2**2*K3*K4 - 1184*K1*K2**2*K3 - 352*K1*K2**2*K5 - 224*K1*K2*K3*K4 - 64*K1*K2*K3*K6 + 6344*K1*K2*K3 + 1240*K1*K3*K4 + 176*K1*K4*K5 - 32*K2**6 + 128*K2**4*K4 - 688*K2**4 - 32*K2**3*K6 - 624*K2**2*K3**2 - 568*K2**2*K4**2 + 2376*K2**2*K4 - 4564*K2**2 + 512*K2*K3*K5 + 296*K2*K4*K6 + 8*K3**2*K6 - 2008*K3**2 - 1084*K4**2 - 80*K5**2 - 28*K6**2 + 4194 |
| 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}], [{1, 6}, {5}, {4}, {3}, {2}], [{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}], [{3, 6}, {5}, {4}, {2}, {1}], [{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}], [{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}], [{5, 6}, {4}, {3}, {2}, {1}], [{6}, {1, 5}, {2, 4}, {3}], [{6}, {1, 5}, {3, 4}, {2}], [{6}, {1, 5}, {4}, {2, 3}], [{6}, {1, 5}, {4}, {3}, {2}], [{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}, {3, 5}, {4}, {2}, {1}], [{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}, {1, 3}, {2}]] |
| If K is slice | False |