| Min(phi) over symmetries of the knot is: [-2,-1,0,1,1,1,-1,1,1,1,2,0,0,1,2,0,1,1,0,0,1] |
| Flat knots (up to 7 crossings) with same phi are :['6.1546'] |
| Arrow polynomial of the knot is: -2*K1**2 - 4*K1*K2 + 2*K1 + K2 + 2*K3 + 2 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.120', '6.213', '6.216', '6.320', '6.322', '6.615', '6.617', '6.891', '6.951', '6.955', '6.1001', '6.1012', '6.1022', '6.1043', '6.1047', '6.1063', '6.1074', '6.1249', '6.1544', '6.1546', '6.1555', '6.1573', '6.1574', '6.1585', '6.1756', '6.1757', '6.1762', '6.1802', '6.1803', '6.1824', '6.1881', '6.1935'] |
| Outer characteristic polynomial of the knot is: t^7+30t^5+73t^3+13t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1546'] |
| 2-strand cable arrow polynomial of the knot is: -272*K1**4 - 64*K1**3*K3 + 512*K1**2*K2**3 - 3968*K1**2*K2**2 - 128*K1**2*K2*K4 + 5384*K1**2*K2 - 80*K1**2*K3**2 - 5028*K1**2 + 448*K1*K2**3*K3 - 736*K1*K2**2*K3 - 128*K1*K2**2*K5 - 288*K1*K2*K3*K4 + 5968*K1*K2*K3 + 504*K1*K3*K4 + 88*K1*K4*K5 - 840*K2**4 - 464*K2**2*K3**2 - 48*K2**2*K4**2 + 1128*K2**2*K4 - 3612*K2**2 + 360*K2*K3*K5 + 32*K2*K4*K6 - 2048*K3**2 - 422*K4**2 - 60*K5**2 - 4*K6**2 + 3764 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1546'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.73745', 'vk6.73861', 'vk6.74202', 'vk6.74824', 'vk6.75662', 'vk6.75864', 'vk6.76383', 'vk6.76881', 'vk6.78677', 'vk6.78864', 'vk6.79235', 'vk6.79712', 'vk6.80291', 'vk6.80418', 'vk6.80723', 'vk6.81076', 'vk6.81626', 'vk6.81808', 'vk6.82000', 'vk6.82321', 'vk6.82371', 'vk6.82731', 'vk6.83229', 'vk6.84246', 'vk6.84327', 'vk6.84408', 'vk6.84493', 'vk6.85651', 'vk6.86539', 'vk6.87565', 'vk6.88282', 'vk6.89407'] |
| 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 | O1O2O3U4O5U2U1O4O6U5U3U6 |
| R3 orbit | {'O1O2O3U4O5U2U1O4O6U5U3U6'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U4U1U5O4O6U3U2O5U6 |
| Gauss code of K* | O1O2O3U4U5U2O6U1O5O4U6U3 |
| Gauss code of -K* | O1O2O3U1U4O5O6U3O4U2U6U5 |
| 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 -1 -1 1 -1 0 2],[ 1 0 0 2 0 1 2],[ 1 0 0 1 1 0 2],[-1 -2 -1 0 0 -1 2],[ 1 0 -1 0 0 0 1],[ 0 -1 0 1 0 0 1],[-2 -2 -2 -2 -1 -1 0]] |
| Primitive based matrix | [[ 0 2 1 0 -1 -1 -1],[-2 0 -2 -1 -1 -2 -2],[-1 2 0 -1 0 -1 -2],[ 0 1 1 0 0 0 -1],[ 1 1 0 0 0 -1 0],[ 1 2 1 0 1 0 0],[ 1 2 2 1 0 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,0,1,1,1,2,1,1,2,2,1,0,1,2,0,0,1,1,0,0] |
| Phi over symmetry | [-2,-1,0,1,1,1,-1,1,1,1,2,0,0,1,2,0,1,1,0,0,1] |
| Phi of -K | [-1,-1,-1,0,1,2,-1,0,1,1,1,0,1,2,2,0,0,1,0,1,-1] |
| Phi of K* | [-2,-1,0,1,1,1,-1,1,1,1,2,0,0,1,2,0,1,1,0,0,1] |
| Phi of -K* | [-1,-1,-1,0,1,2,-1,0,0,0,1,0,0,1,2,1,2,2,1,1,2] |
| Symmetry type of based matrix | c |
| u-polynomial | -t^2+2t |
| Normalized Jones-Krushkal polynomial | 5z^2+22z+25 |
| Enhanced Jones-Krushkal polynomial | -2w^4z^2+7w^3z^2-4w^3z+26w^2z+25w |
| Inner characteristic polynomial | t^6+22t^4+32t^2+1 |
| Outer characteristic polynomial | t^7+30t^5+73t^3+13t |
| Flat arrow polynomial | -2*K1**2 - 4*K1*K2 + 2*K1 + K2 + 2*K3 + 2 |
| 2-strand cable arrow polynomial | -272*K1**4 - 64*K1**3*K3 + 512*K1**2*K2**3 - 3968*K1**2*K2**2 - 128*K1**2*K2*K4 + 5384*K1**2*K2 - 80*K1**2*K3**2 - 5028*K1**2 + 448*K1*K2**3*K3 - 736*K1*K2**2*K3 - 128*K1*K2**2*K5 - 288*K1*K2*K3*K4 + 5968*K1*K2*K3 + 504*K1*K3*K4 + 88*K1*K4*K5 - 840*K2**4 - 464*K2**2*K3**2 - 48*K2**2*K4**2 + 1128*K2**2*K4 - 3612*K2**2 + 360*K2*K3*K5 + 32*K2*K4*K6 - 2048*K3**2 - 422*K4**2 - 60*K5**2 - 4*K6**2 + 3764 |
| 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}], [{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}, {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}, {1, 4}, {3}, {2}], [{6}, {5}, {2, 4}, {1, 3}], [{6}, {5}, {3, 4}, {1, 2}]] |
| If K is slice | False |