| Min(phi) over symmetries of the knot is: [-4,0,0,0,1,3,1,2,3,1,4,0,0,1,1,0,1,2,1,3,-1] |
| Flat knots (up to 7 crossings) with same phi are :['6.429'] |
| Arrow polynomial of the knot is: -2*K1*K2 + K1 - 2*K2**2 + K3 + K4 + 2 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.95', '6.107', '6.276', '6.292', '6.394', '6.429', '6.463'] |
| Outer characteristic polynomial of the knot is: t^7+79t^5+62t^3+6t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.429'] |
| 2-strand cable arrow polynomial of the knot is: -144*K1**4 + 96*K1**3*K3*K4 - 768*K1**2*K2*K4 + 768*K1**2*K2 - 208*K1**2*K3**2 - 704*K1**2*K4**2 - 1660*K1**2 + 96*K1*K2*K3*K4**2 - 416*K1*K2*K3*K4 + 1432*K1*K2*K3 - 64*K1*K2*K4*K7 + 1912*K1*K3*K4 + 744*K1*K4*K5 - 72*K2**2*K4**2 + 680*K2**2*K4 - 1182*K2**2 - 32*K2*K3**2*K4 + 128*K2*K3*K5 + 64*K2*K4*K6 + 8*K2*K5*K7 - 48*K3**2*K4**2 - 1000*K3**2 + 32*K3*K4*K7 - 8*K4**4 + 8*K4**2*K8 - 992*K4**2 - 168*K5**2 - 2*K6**2 - 4*K7**2 - 2*K8**2 + 1504 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.429'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.19955', 'vk6.20092', 'vk6.21208', 'vk6.21374', 'vk6.26944', 'vk6.27157', 'vk6.28692', 'vk6.28846', 'vk6.38360', 'vk6.38557', 'vk6.40512', 'vk6.40754', 'vk6.45223', 'vk6.45454', 'vk6.47042', 'vk6.47196', 'vk6.56751', 'vk6.56909', 'vk6.57860', 'vk6.58047', 'vk6.61210', 'vk6.61442', 'vk6.62436', 'vk6.62599', 'vk6.66463', 'vk6.66613', 'vk6.67244', 'vk6.67404', 'vk6.69109', 'vk6.69261', 'vk6.69884', 'vk6.70002'] |
| 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 | O1O2O3O4O5U6U1O6U4U3U2U5 |
| R3 orbit | {'O1O2O3O4O5U6U1O6U4U3U2U5'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4O5U1U4U3U2O6U5U6 |
| Gauss code of K* | O1O2O3O4U5U3U2U1U4O6O5U6 |
| Gauss code of -K* | O1O2O3O4U5O6O5U1U4U3U2U6 |
| 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 0 0 0 4 -1],[ 3 0 2 1 0 3 3],[ 0 -2 0 0 0 3 0],[ 0 -1 0 0 0 2 0],[ 0 0 0 0 0 1 0],[-4 -3 -3 -2 -1 0 -4],[ 1 -3 0 0 0 4 0]] |
| Primitive based matrix | [[ 0 4 0 0 0 -1 -3],[-4 0 -1 -2 -3 -4 -3],[ 0 1 0 0 0 0 0],[ 0 2 0 0 0 0 -1],[ 0 3 0 0 0 0 -2],[ 1 4 0 0 0 0 -3],[ 3 3 0 1 2 3 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-4,0,0,0,1,3,1,2,3,4,3,0,0,0,0,0,0,1,0,2,3] |
| Phi over symmetry | [-4,0,0,0,1,3,1,2,3,1,4,0,0,1,1,0,1,2,1,3,-1] |
| Phi of -K | [-3,-1,0,0,0,4,-1,1,2,3,4,1,1,1,1,0,0,1,0,2,3] |
| Phi of K* | [-4,0,0,0,1,3,1,2,3,1,4,0,0,1,1,0,1,2,1,3,-1] |
| Phi of -K* | [-3,-1,0,0,0,4,3,0,1,2,3,0,0,0,4,0,0,1,0,2,3] |
| Symmetry type of based matrix | c |
| u-polynomial | -t^4+t^3+t |
| Normalized Jones-Krushkal polynomial | z^2+6z+9 |
| Enhanced Jones-Krushkal polynomial | -4w^4z^2+5w^3z^2-12w^3z+18w^2z+9w |
| Inner characteristic polynomial | t^6+53t^4+20t^2 |
| Outer characteristic polynomial | t^7+79t^5+62t^3+6t |
| Flat arrow polynomial | -2*K1*K2 + K1 - 2*K2**2 + K3 + K4 + 2 |
| 2-strand cable arrow polynomial | -144*K1**4 + 96*K1**3*K3*K4 - 768*K1**2*K2*K4 + 768*K1**2*K2 - 208*K1**2*K3**2 - 704*K1**2*K4**2 - 1660*K1**2 + 96*K1*K2*K3*K4**2 - 416*K1*K2*K3*K4 + 1432*K1*K2*K3 - 64*K1*K2*K4*K7 + 1912*K1*K3*K4 + 744*K1*K4*K5 - 72*K2**2*K4**2 + 680*K2**2*K4 - 1182*K2**2 - 32*K2*K3**2*K4 + 128*K2*K3*K5 + 64*K2*K4*K6 + 8*K2*K5*K7 - 48*K3**2*K4**2 - 1000*K3**2 + 32*K3*K4*K7 - 8*K4**4 + 8*K4**2*K8 - 992*K4**2 - 168*K5**2 - 2*K6**2 - 4*K7**2 - 2*K8**2 + 1504 |
| 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}], [{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}, {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}, {2, 4}, {3}, {1}], [{6}, {5}, {3, 4}, {1, 2}]] |
| If K is slice | False |