| Min(phi) over symmetries of the knot is: [-4,0,0,0,1,3,1,2,3,1,4,0,0,0,0,0,0,1,0,2,-1] |
| Flat knots (up to 7 crossings) with same phi are :['6.176'] |
| Arrow polynomial of the knot is: -2*K1**2 - 2*K1*K2 - 2*K1*K3 + K1 + 2*K2 + K3 + K4 + 2 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.62', '6.176', '6.181', '6.194', '6.228', '6.267', '6.268', '6.449'] |
| Outer characteristic polynomial of the knot is: t^7+91t^5+59t^3+6t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.176'] |
| 2-strand cable arrow polynomial of the knot is: -144*K1**4 + 192*K1**3*K2*K3 - 288*K1**2*K2**2 + 1696*K1**2*K2 - 880*K1**2*K3**2 - 192*K1**2*K3*K5 - 2152*K1**2 - 1472*K1*K2**2*K3 - 32*K1*K2*K3*K6 + 3152*K1*K2*K3 - 32*K1*K2*K5*K6 + 1632*K1*K3*K4 + 160*K1*K4*K5 + 16*K1*K5*K6 + 16*K1*K6*K7 - 8*K2**4 - 32*K2**3*K6 - 512*K2**2*K3**2 - 8*K2**2*K4**2 + 704*K2**2*K4 - 8*K2**2*K6**2 - 2050*K2**2 + 544*K2*K3*K5 + 80*K2*K4*K6 + 16*K2*K5*K7 + 8*K2*K6*K8 + 16*K3**2*K6 - 1552*K3**2 - 580*K4**2 - 176*K5**2 - 38*K6**2 - 8*K7**2 - 2*K8**2 + 1932 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.176'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.17123', 'vk6.17364', 'vk6.20259', 'vk6.21568', 'vk6.23523', 'vk6.23856', 'vk6.27503', 'vk6.29091', 'vk6.35684', 'vk6.36111', 'vk6.38914', 'vk6.41119', 'vk6.43031', 'vk6.43337', 'vk6.45665', 'vk6.47394', 'vk6.55272', 'vk6.55518', 'vk6.57084', 'vk6.58240', 'vk6.59689', 'vk6.60026', 'vk6.61637', 'vk6.62816', 'vk6.65077', 'vk6.65264', 'vk6.66719', 'vk6.67577', 'vk6.68331', 'vk6.68477', 'vk6.69365', 'vk6.70107'] |
| 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 | O1O2O3O4O5U1O6U5U4U3U6U2 |
| R3 orbit | {'O1O2O3O4O5U1O6U5U4U3U6U2'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4O5U4U6U3U2U1O6U5 |
| Gauss code of K* | O1O2O3O4O5U6U5U3U2U1O6U4 |
| Gauss code of -K* | O1O2O3O4O5U2O6U5U4U3U1U6 |
| 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 -4 1 0 0 0 3],[ 4 0 4 3 2 1 3],[-1 -4 0 -1 -1 -1 3],[ 0 -3 1 0 0 0 3],[ 0 -2 1 0 0 0 2],[ 0 -1 1 0 0 0 1],[-3 -3 -3 -3 -2 -1 0]] |
| Primitive based matrix | [[ 0 3 1 0 0 0 -4],[-3 0 -3 -1 -2 -3 -3],[-1 3 0 -1 -1 -1 -4],[ 0 1 1 0 0 0 -1],[ 0 2 1 0 0 0 -2],[ 0 3 1 0 0 0 -3],[ 4 3 4 1 2 3 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-3,-1,0,0,0,4,3,1,2,3,3,1,1,1,4,0,0,1,0,2,3] |
| Phi over symmetry | [-4,0,0,0,1,3,1,2,3,1,4,0,0,0,0,0,0,1,0,2,-1] |
| Phi of -K | [-4,0,0,0,1,3,1,2,3,1,4,0,0,0,0,0,0,1,0,2,-1] |
| Phi of K* | [-3,-1,0,0,0,4,-1,0,1,2,4,0,0,0,1,0,0,1,0,2,3] |
| Phi of -K* | [-4,0,0,0,1,3,1,2,3,4,3,0,0,1,1,0,1,2,1,3,3] |
| Symmetry type of based matrix | c |
| u-polynomial | t^4-t^3-t |
| Normalized Jones-Krushkal polynomial | 5z+11 |
| Enhanced Jones-Krushkal polynomial | -4w^4z^2+4w^3z^2-12w^3z+17w^2z+11w |
| Inner characteristic polynomial | t^6+65t^4+17t^2 |
| Outer characteristic polynomial | t^7+91t^5+59t^3+6t |
| Flat arrow polynomial | -2*K1**2 - 2*K1*K2 - 2*K1*K3 + K1 + 2*K2 + K3 + K4 + 2 |
| 2-strand cable arrow polynomial | -144*K1**4 + 192*K1**3*K2*K3 - 288*K1**2*K2**2 + 1696*K1**2*K2 - 880*K1**2*K3**2 - 192*K1**2*K3*K5 - 2152*K1**2 - 1472*K1*K2**2*K3 - 32*K1*K2*K3*K6 + 3152*K1*K2*K3 - 32*K1*K2*K5*K6 + 1632*K1*K3*K4 + 160*K1*K4*K5 + 16*K1*K5*K6 + 16*K1*K6*K7 - 8*K2**4 - 32*K2**3*K6 - 512*K2**2*K3**2 - 8*K2**2*K4**2 + 704*K2**2*K4 - 8*K2**2*K6**2 - 2050*K2**2 + 544*K2*K3*K5 + 80*K2*K4*K6 + 16*K2*K5*K7 + 8*K2*K6*K8 + 16*K3**2*K6 - 1552*K3**2 - 580*K4**2 - 176*K5**2 - 38*K6**2 - 8*K7**2 - 2*K8**2 + 1932 |
| 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}], [{2, 6}, {5}, {4}, {3}, {1}], [{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}], [{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}, {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}, {3}, {1, 2}]] |
| If K is slice | False |