| Min(phi) over symmetries of the knot is: [-2,-1,0,0,1,2,-1,0,1,2,3,0,1,1,1,0,0,1,0,1,1] |
| Flat knots (up to 7 crossings) with same phi are :['6.1519'] |
| Arrow polynomial of the knot is: -8*K1**2 - 4*K1*K2 + 2*K1 + 4*K2 + 2*K3 + 5 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.235', '6.379', '6.411', '6.547', '6.811', '6.818', '6.823', '6.897', '6.898', '6.1008', '6.1053', '6.1109', '6.1110', '6.1130', '6.1222', '6.1239', '6.1303', '6.1307', '6.1342', '6.1491', '6.1495', '6.1496', '6.1519', '6.1592', '6.1593', '6.1642', '6.1652', '6.1653', '6.1671', '6.1673', '6.1717'] |
| Outer characteristic polynomial of the knot is: t^7+31t^5+25t^3+5t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1519'] |
| 2-strand cable arrow polynomial of the knot is: -128*K1**6 + 448*K1**4*K2 - 3504*K1**4 + 352*K1**3*K2*K3 + 64*K1**3*K3*K4 - 928*K1**3*K3 - 2048*K1**2*K2**2 - 512*K1**2*K2*K4 + 7456*K1**2*K2 - 688*K1**2*K3**2 - 144*K1**2*K4**2 - 4584*K1**2 - 448*K1*K2**2*K3 - 96*K1*K2*K3*K4 + 5200*K1*K2*K3 + 1432*K1*K3*K4 + 192*K1*K4*K5 - 64*K2**4 - 64*K2**2*K3**2 - 16*K2**2*K4**2 + 656*K2**2*K4 - 4044*K2**2 + 160*K2*K3*K5 + 32*K2*K4*K6 - 2052*K3**2 - 692*K4**2 - 108*K5**2 - 12*K6**2 + 4138 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1519'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.3658', 'vk6.3753', 'vk6.3944', 'vk6.4039', 'vk6.4476', 'vk6.4571', 'vk6.5862', 'vk6.5989', 'vk6.7149', 'vk6.7324', 'vk6.7415', 'vk6.7907', 'vk6.8026', 'vk6.9341', 'vk6.17910', 'vk6.18007', 'vk6.18763', 'vk6.24445', 'vk6.24888', 'vk6.25349', 'vk6.37510', 'vk6.43880', 'vk6.44243', 'vk6.44546', 'vk6.48298', 'vk6.48361', 'vk6.50087', 'vk6.50197', 'vk6.50568', 'vk6.50631', 'vk6.55855', 'vk6.60727'] |
| 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 | O1O2O3U2O4U3U5O6O5U1U6U4 |
| R3 orbit | {'O1O2O3U2O4U3U5O6O5U1U6U4'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U4U5U3O6O5U6U1O4U2 |
| Gauss code of K* | O1O2O3U1U4U5O4U3O5O6U2U6 |
| Gauss code of -K* | O1O2O3U4U2O4O5U1O6U5U6U3 |
| 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 -2 -1 0 2 1 0],[ 2 0 -1 1 3 2 0],[ 1 1 0 1 1 1 0],[ 0 -1 -1 0 1 0 0],[-2 -3 -1 -1 0 -1 -1],[-1 -2 -1 0 1 0 0],[ 0 0 0 0 1 0 0]] |
| Primitive based matrix | [[ 0 2 1 0 0 -1 -2],[-2 0 -1 -1 -1 -1 -3],[-1 1 0 0 0 -1 -2],[ 0 1 0 0 0 0 0],[ 0 1 0 0 0 -1 -1],[ 1 1 1 0 1 0 1],[ 2 3 2 0 1 -1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,0,0,1,2,1,1,1,1,3,0,0,1,2,0,0,0,1,1,-1] |
| Phi over symmetry | [-2,-1,0,0,1,2,-1,0,1,2,3,0,1,1,1,0,0,1,0,1,1] |
| Phi of -K | [-2,-1,0,0,1,2,2,1,2,1,1,0,1,1,2,0,1,1,1,1,0] |
| Phi of K* | [-2,-1,0,0,1,2,0,1,1,2,1,1,1,1,1,0,0,1,1,2,2] |
| Phi of -K* | [-2,-1,0,0,1,2,-1,0,1,2,3,0,1,1,1,0,0,1,0,1,1] |
| Symmetry type of based matrix | c |
| u-polynomial | 0 |
| Normalized Jones-Krushkal polynomial | 17z+35 |
| Enhanced Jones-Krushkal polynomial | 17w^2z+35w |
| Inner characteristic polynomial | t^6+21t^4+11t^2+1 |
| Outer characteristic polynomial | t^7+31t^5+25t^3+5t |
| Flat arrow polynomial | -8*K1**2 - 4*K1*K2 + 2*K1 + 4*K2 + 2*K3 + 5 |
| 2-strand cable arrow polynomial | -128*K1**6 + 448*K1**4*K2 - 3504*K1**4 + 352*K1**3*K2*K3 + 64*K1**3*K3*K4 - 928*K1**3*K3 - 2048*K1**2*K2**2 - 512*K1**2*K2*K4 + 7456*K1**2*K2 - 688*K1**2*K3**2 - 144*K1**2*K4**2 - 4584*K1**2 - 448*K1*K2**2*K3 - 96*K1*K2*K3*K4 + 5200*K1*K2*K3 + 1432*K1*K3*K4 + 192*K1*K4*K5 - 64*K2**4 - 64*K2**2*K3**2 - 16*K2**2*K4**2 + 656*K2**2*K4 - 4044*K2**2 + 160*K2*K3*K5 + 32*K2*K4*K6 - 2052*K3**2 - 692*K4**2 - 108*K5**2 - 12*K6**2 + 4138 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {3, 5}, {2, 4}], [{1, 6}, {4, 5}, {2, 3}], [{3, 6}, {1, 5}, {2, 4}], [{3, 6}, {2, 5}, {1, 4}], [{3, 6}, {4, 5}, {1, 2}], [{4, 6}, {1, 5}, {2, 3}], [{4, 6}, {3, 5}, {1, 2}]] |
| If K is slice | False |