| Min(phi) over symmetries of the knot is: [-2,-2,1,1,1,1,0,0,1,2,2,1,1,1,2,-1,-1,-1,0,0,-1] |
| Flat knots (up to 7 crossings) with same phi are :['6.1651'] |
| Arrow polynomial of the knot is: 4*K1**3 - 4*K1*K2 - K1 + K3 + 1 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.395', '6.430', '6.440', '6.548', '6.551', '6.774', '6.832', '6.887', '6.908', '6.911', '6.1205', '6.1332', '6.1339', '6.1341', '6.1346', '6.1382', '6.1488', '6.1651', '6.1655', '6.1686'] |
| Outer characteristic polynomial of the knot is: t^7+32t^5+52t^3+15t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1651'] |
| 2-strand cable arrow polynomial of the knot is: -576*K1**2*K2**4 + 608*K1**2*K2**3 + 128*K1**2*K2**2*K4 - 5328*K1**2*K2**2 - 352*K1**2*K2*K4 + 4992*K1**2*K2 - 64*K1**2*K4**2 - 3504*K1**2 + 832*K1*K2**3*K3 - 832*K1*K2**2*K3 - 608*K1*K2**2*K5 - 320*K1*K2*K3*K4 + 5472*K1*K2*K3 + 432*K1*K3*K4 + 368*K1*K4*K5 - 288*K2**6 + 448*K2**4*K4 - 2656*K2**4 - 128*K2**3*K6 - 240*K2**2*K3**2 - 112*K2**2*K4**2 + 2888*K2**2*K4 - 2358*K2**2 + 544*K2*K3*K5 + 48*K2*K4*K6 - 1320*K3**2 - 748*K4**2 - 232*K5**2 - 2*K6**2 + 2906 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1651'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.17538', 'vk6.17543', 'vk6.17595', 'vk6.17598', 'vk6.24046', 'vk6.24051', 'vk6.24139', 'vk6.24141', 'vk6.36326', 'vk6.36335', 'vk6.36396', 'vk6.36400', 'vk6.43451', 'vk6.43456', 'vk6.43497', 'vk6.43500', 'vk6.55628', 'vk6.55641', 'vk6.55656', 'vk6.55664', 'vk6.60146', 'vk6.60156', 'vk6.60204', 'vk6.60214', 'vk6.65333', 'vk6.65348', 'vk6.65367', 'vk6.65378', 'vk6.68503', 'vk6.68512', 'vk6.68526', 'vk6.68534'] |
| 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 | O1O2O3U1O4U5U3U2O5O6U4U6 |
| R3 orbit | {'O1O2O3U1O4U5U3U2O5O6U4U6'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U4U5O4O6U2U1U6O5U3 |
| Gauss code of K* | O1O2O3U1U4O5O4U6U3U2O6U5 |
| Gauss code of -K* | O1O2O3U4O5U2U1U5O6O4U6U3 |
| 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 1 1 -2 1],[ 2 0 2 1 2 0 0],[-1 -2 0 0 1 -2 1],[-1 -1 0 0 0 -1 1],[-1 -2 -1 0 0 -1 1],[ 2 0 2 1 1 0 1],[-1 0 -1 -1 -1 -1 0]] |
| Primitive based matrix | [[ 0 1 1 1 1 -2 -2],[-1 0 1 1 0 -2 -2],[-1 -1 0 1 0 -1 -2],[-1 -1 -1 0 -1 -1 0],[-1 0 0 1 0 -1 -1],[ 2 2 1 1 1 0 0],[ 2 2 2 0 1 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-1,-1,-1,-1,2,2,-1,-1,0,2,2,-1,0,1,2,1,1,0,1,1,0] |
| Phi over symmetry | [-2,-2,1,1,1,1,0,0,1,2,2,1,1,1,2,-1,-1,-1,0,0,-1] |
| Phi of -K | [-2,-2,1,1,1,1,0,1,1,2,3,1,2,2,2,-1,0,-1,0,-1,-1] |
| Phi of K* | [-1,-1,-1,-1,2,2,-1,-1,-1,2,3,-1,0,2,1,0,1,1,2,2,0] |
| Phi of -K* | [-2,-2,1,1,1,1,0,0,1,2,2,1,1,1,2,-1,-1,-1,0,0,-1] |
| Symmetry type of based matrix | c |
| u-polynomial | 2t^2-4t |
| Normalized Jones-Krushkal polynomial | 6z^2+19z+15 |
| Enhanced Jones-Krushkal polynomial | -4w^4z^2+10w^3z^2-8w^3z+27w^2z+15w |
| Inner characteristic polynomial | t^6+20t^4+24t^2 |
| Outer characteristic polynomial | t^7+32t^5+52t^3+15t |
| Flat arrow polynomial | 4*K1**3 - 4*K1*K2 - K1 + K3 + 1 |
| 2-strand cable arrow polynomial | -576*K1**2*K2**4 + 608*K1**2*K2**3 + 128*K1**2*K2**2*K4 - 5328*K1**2*K2**2 - 352*K1**2*K2*K4 + 4992*K1**2*K2 - 64*K1**2*K4**2 - 3504*K1**2 + 832*K1*K2**3*K3 - 832*K1*K2**2*K3 - 608*K1*K2**2*K5 - 320*K1*K2*K3*K4 + 5472*K1*K2*K3 + 432*K1*K3*K4 + 368*K1*K4*K5 - 288*K2**6 + 448*K2**4*K4 - 2656*K2**4 - 128*K2**3*K6 - 240*K2**2*K3**2 - 112*K2**2*K4**2 + 2888*K2**2*K4 - 2358*K2**2 + 544*K2*K3*K5 + 48*K2*K4*K6 - 1320*K3**2 - 748*K4**2 - 232*K5**2 - 2*K6**2 + 2906 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{3, 6}, {1, 5}, {2, 4}]] |
| If K is slice | False |