| Min(phi) over symmetries of the knot is: [-2,-1,0,1,1,1,0,2,1,2,3,0,0,1,2,2,1,0,0,-1,-1] |
| Flat knots (up to 7 crossings) with same phi are :['6.1757'] |
| 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+38t^5+108t^3+12t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1757'] |
| 2-strand cable arrow polynomial of the knot is: -256*K1**4*K2**2 + 224*K1**4*K2 - 1232*K1**4 + 768*K1**3*K2*K3 - 672*K1**3*K3 + 288*K1**2*K2**3 - 3168*K1**2*K2**2 - 928*K1**2*K2*K4 + 5208*K1**2*K2 - 400*K1**2*K3**2 - 3812*K1**2 + 64*K1*K2**3*K3 - 384*K1*K2**2*K3 - 64*K1*K2**2*K5 - 64*K1*K2*K3*K4 + 5032*K1*K2*K3 + 960*K1*K3*K4 + 32*K1*K4*K5 - 200*K2**4 - 112*K2**2*K3**2 - 48*K2**2*K4**2 + 672*K2**2*K4 - 2900*K2**2 + 112*K2*K3*K5 + 32*K2*K4*K6 - 1576*K3**2 - 438*K4**2 - 20*K5**2 - 4*K6**2 + 2884 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1757'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.16923', 'vk6.17166', 'vk6.20227', 'vk6.21521', 'vk6.23313', 'vk6.23609', 'vk6.27433', 'vk6.29042', 'vk6.35350', 'vk6.35775', 'vk6.38850', 'vk6.41040', 'vk6.42835', 'vk6.43115', 'vk6.45607', 'vk6.47364', 'vk6.55077', 'vk6.55329', 'vk6.57063', 'vk6.58190', 'vk6.59466', 'vk6.59759', 'vk6.61587', 'vk6.62765', 'vk6.64916', 'vk6.65128', 'vk6.66688', 'vk6.67530', 'vk6.68217', 'vk6.68361', 'vk6.69336', 'vk6.70087'] |
| 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 | O1O2O3U4U5O4O6U2U1O5U3U6 |
| R3 orbit | {'O1O2O3U4U5O4O6U2U1O5U3U6'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U4U1O5U3U2O4O6U5U6 |
| Gauss code of K* | O1O2U3O4O5U2U1U4O6O3U6U5 |
| Gauss code of -K* | O1O2U3O4O5U1U6O3O6U2U5U4 |
| 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 1 1 1 2],[ 1 0 0 0 1 2 1],[-1 -1 0 0 -2 0 0],[ 1 -1 -1 2 0 0 3],[ 0 -1 -2 0 0 0 2],[-2 -2 -1 0 -3 -2 0]] |
| Primitive based matrix | [[ 0 2 1 0 -1 -1 -1],[-2 0 0 -2 -1 -2 -3],[-1 0 0 0 0 -1 -2],[ 0 2 0 0 -2 -1 0],[ 1 1 0 2 0 0 1],[ 1 2 1 1 0 0 1],[ 1 3 2 0 -1 -1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,0,1,1,1,0,2,1,2,3,0,0,1,2,2,1,0,0,-1,-1] |
| Phi over symmetry | [-2,-1,0,1,1,1,0,2,1,2,3,0,0,1,2,2,1,0,0,-1,-1] |
| Phi of -K | [-1,-1,-1,0,1,2,-1,0,-1,2,2,1,1,0,0,0,1,1,1,0,1] |
| Phi of K* | [-2,-1,0,1,1,1,1,0,0,1,2,1,0,1,2,1,0,-1,-1,-1,0] |
| Phi of -K* | [-1,-1,-1,0,1,2,-1,-1,0,2,3,0,1,1,2,2,0,1,0,2,0] |
| 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^2-2w^3z+24w^2z+25w |
| Inner characteristic polynomial | t^6+30t^4+79t^2+4 |
| Outer characteristic polynomial | t^7+38t^5+108t^3+12t |
| Flat arrow polynomial | -2*K1**2 - 4*K1*K2 + 2*K1 + K2 + 2*K3 + 2 |
| 2-strand cable arrow polynomial | -256*K1**4*K2**2 + 224*K1**4*K2 - 1232*K1**4 + 768*K1**3*K2*K3 - 672*K1**3*K3 + 288*K1**2*K2**3 - 3168*K1**2*K2**2 - 928*K1**2*K2*K4 + 5208*K1**2*K2 - 400*K1**2*K3**2 - 3812*K1**2 + 64*K1*K2**3*K3 - 384*K1*K2**2*K3 - 64*K1*K2**2*K5 - 64*K1*K2*K3*K4 + 5032*K1*K2*K3 + 960*K1*K3*K4 + 32*K1*K4*K5 - 200*K2**4 - 112*K2**2*K3**2 - 48*K2**2*K4**2 + 672*K2**2*K4 - 2900*K2**2 + 112*K2*K3*K5 + 32*K2*K4*K6 - 1576*K3**2 - 438*K4**2 - 20*K5**2 - 4*K6**2 + 2884 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {2, 5}, {3, 4}], [{2, 6}, {1, 5}, {3, 4}], [{2, 6}, {3, 5}, {1, 4}], [{5, 6}, {3, 4}, {1, 2}]] |
| If K is slice | False |