| Min(phi) over symmetries of the knot is: [-2,-1,-1,1,1,2,-1,0,1,2,3,1,1,1,1,1,1,2,0,0,1] |
| Flat knots (up to 7 crossings) with same phi are :['6.1110'] |
| 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+34t^5+28t^3+5t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1110'] |
| 2-strand cable arrow polynomial of the knot is: -192*K1**6 - 384*K1**4*K2**2 + 1792*K1**4*K2 - 5392*K1**4 + 1056*K1**3*K2*K3 + 32*K1**3*K3*K4 - 1376*K1**3*K3 + 384*K1**2*K2**3 - 5984*K1**2*K2**2 - 736*K1**2*K2*K4 + 10624*K1**2*K2 - 1200*K1**2*K3**2 - 144*K1**2*K4**2 - 4972*K1**2 + 96*K1*K2**3*K3 - 768*K1*K2**2*K3 - 64*K1*K2**2*K5 - 128*K1*K2*K3*K4 + 7808*K1*K2*K3 + 1736*K1*K3*K4 + 208*K1*K4*K5 - 288*K2**4 - 128*K2**2*K3**2 - 16*K2**2*K4**2 + 704*K2**2*K4 - 4548*K2**2 + 176*K2*K3*K5 + 32*K2*K4*K6 - 2352*K3**2 - 644*K4**2 - 92*K5**2 - 12*K6**2 + 4770 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1110'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.4209', 'vk6.4288', 'vk6.5470', 'vk6.5581', 'vk6.7570', 'vk6.7658', 'vk6.9074', 'vk6.9153', 'vk6.11163', 'vk6.12247', 'vk6.12354', 'vk6.19381', 'vk6.19674', 'vk6.19781', 'vk6.26163', 'vk6.26214', 'vk6.26579', 'vk6.26659', 'vk6.30761', 'vk6.31962', 'vk6.38163', 'vk6.38194', 'vk6.44820', 'vk6.44935', 'vk6.48519', 'vk6.49216', 'vk6.49323', 'vk6.50306', 'vk6.52749', 'vk6.63593', 'vk6.66327', 'vk6.66350'] |
| 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 | O1O2O3O4U2U4O5U6U1O6U3U5 |
| R3 orbit | {'O1O2O3O4U2U4O5U6U1O6U3U5'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U5U2O6U4U6O5U1U3 |
| Gauss code of K* | O1O2U3O4O5U4O6O3U5U1U6U2 |
| Gauss code of -K* | O1O2U3O4O3U1O5O6U5U2U6U4 |
| 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 -2 1 1 2 -1],[ 1 0 -1 1 1 1 1],[ 2 1 0 2 1 1 2],[-1 -1 -2 0 0 1 -1],[-1 -1 -1 0 0 0 -1],[-2 -1 -1 -1 0 0 -2],[ 1 -1 -2 1 1 2 0]] |
| Primitive based matrix | [[ 0 2 1 1 -1 -1 -2],[-2 0 0 -1 -1 -2 -1],[-1 0 0 0 -1 -1 -1],[-1 1 0 0 -1 -1 -2],[ 1 1 1 1 0 1 -1],[ 1 2 1 1 -1 0 -2],[ 2 1 1 2 1 2 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,-1,1,1,2,0,1,1,2,1,0,1,1,1,1,1,2,-1,1,2] |
| Phi over symmetry | [-2,-1,-1,1,1,2,-1,0,1,2,3,1,1,1,1,1,1,2,0,0,1] |
| Phi of -K | [-2,-1,-1,1,1,2,-1,0,1,2,3,1,1,1,1,1,1,2,0,0,1] |
| Phi of K* | [-2,-1,-1,1,1,2,0,1,1,2,3,0,1,1,1,1,1,2,-1,-1,0] |
| Phi of -K* | [-2,-1,-1,1,1,2,1,2,1,2,1,1,1,1,1,1,1,2,0,0,1] |
| Symmetry type of based matrix | c |
| u-polynomial | 0 |
| Normalized Jones-Krushkal polynomial | 3z^2+24z+37 |
| Enhanced Jones-Krushkal polynomial | 3w^3z^2+24w^2z+37w |
| Inner characteristic polynomial | t^6+22t^4+10t^2+1 |
| Outer characteristic polynomial | t^7+34t^5+28t^3+5t |
| Flat arrow polynomial | -8*K1**2 - 4*K1*K2 + 2*K1 + 4*K2 + 2*K3 + 5 |
| 2-strand cable arrow polynomial | -192*K1**6 - 384*K1**4*K2**2 + 1792*K1**4*K2 - 5392*K1**4 + 1056*K1**3*K2*K3 + 32*K1**3*K3*K4 - 1376*K1**3*K3 + 384*K1**2*K2**3 - 5984*K1**2*K2**2 - 736*K1**2*K2*K4 + 10624*K1**2*K2 - 1200*K1**2*K3**2 - 144*K1**2*K4**2 - 4972*K1**2 + 96*K1*K2**3*K3 - 768*K1*K2**2*K3 - 64*K1*K2**2*K5 - 128*K1*K2*K3*K4 + 7808*K1*K2*K3 + 1736*K1*K3*K4 + 208*K1*K4*K5 - 288*K2**4 - 128*K2**2*K3**2 - 16*K2**2*K4**2 + 704*K2**2*K4 - 4548*K2**2 + 176*K2*K3*K5 + 32*K2*K4*K6 - 2352*K3**2 - 644*K4**2 - 92*K5**2 - 12*K6**2 + 4770 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{2, 6}, {3, 5}, {1, 4}], [{2, 6}, {4, 5}, {1, 3}], [{3, 6}, {2, 5}, {1, 4}], [{4, 6}, {2, 5}, {1, 3}], [{5, 6}, {1, 4}, {2, 3}], [{5, 6}, {2, 4}, {1, 3}]] |
| If K is slice | False |