| Min(phi) over symmetries of the knot is: [-3,-2,-2,2,2,3,-1,0,2,4,4,0,0,2,1,1,3,3,-1,0,1] |
| Flat knots (up to 7 crossings) with same phi are :['6.809'] |
| Arrow polynomial of the knot is: 4*K1**3 - 8*K1**2 - 4*K1*K2 - K1 + 4*K2 + K3 + 5 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.315', '6.337', '6.389', '6.418', '6.599', '6.675', '6.686', '6.688', '6.746', '6.747', '6.809', '6.1034', '6.1128', '6.1133', '6.1334', '6.1363', '6.1489', '6.1539', '6.1564', '6.1821', '6.1863'] |
| Outer characteristic polynomial of the knot is: t^7+105t^5+108t^3 |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.809'] |
| 2-strand cable arrow polynomial of the knot is: -64*K1**4*K2**2 + 224*K1**4*K2 - 736*K1**4 + 32*K1**3*K2*K3 + 224*K1**2*K2**3 - 1440*K1**2*K2**2 + 2400*K1**2*K2 - 256*K1**2*K3**2 - 32*K1**2*K4**2 - 2032*K1**2 + 96*K1*K2**3*K3 + 1960*K1*K2*K3 + 448*K1*K3*K4 + 80*K1*K4*K5 + 8*K1*K5*K6 - 32*K2**6 + 32*K2**4*K4 - 368*K2**4 - 160*K2**2*K3**2 - 16*K2**2*K4**2 + 376*K2**2*K4 - 1454*K2**2 + 128*K2*K3*K5 + 16*K2*K4*K6 - 808*K3**2 - 324*K4**2 - 72*K5**2 - 10*K6**2 + 1778 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.809'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.71391', 'vk6.71452', 'vk6.71913', 'vk6.71974', 'vk6.72465', 'vk6.72614', 'vk6.72733', 'vk6.72824', 'vk6.72888', 'vk6.73043', 'vk6.74222', 'vk6.74362', 'vk6.74420', 'vk6.74851', 'vk6.75035', 'vk6.76605', 'vk6.76900', 'vk6.77048', 'vk6.77414', 'vk6.77767', 'vk6.77818', 'vk6.79272', 'vk6.79408', 'vk6.79746', 'vk6.79824', 'vk6.79877', 'vk6.80854', 'vk6.80904', 'vk6.81387', 'vk6.85513', 'vk6.87216', 'vk6.89258'] |
| 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 | O1O2O3O4U1O5U2U6U5U4O6U3 |
| R3 orbit | {'O1O2O3O4U1O5U2U6U5U4O6U3'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U2O5U1U6U5U3O6U4 |
| Gauss code of K* | O1O2O3O4U2O5U6U1U5U4O6U3 |
| Gauss code of -K* | O1O2O3O4U2O5U1U6U4U5O6U3 |
| Diagrammatic symmetry type | c |
| Flat genus of the diagram | 2 |
| If K is checkerboard colorable | False |
| If K is almost classical | False |
| Based matrix from Gauss code | [[ 0 -3 -2 2 3 2 -2],[ 3 0 1 3 2 1 2],[ 2 -1 0 3 2 1 0],[-2 -3 -3 0 1 1 -4],[-3 -2 -2 -1 0 0 -4],[-2 -1 -1 -1 0 0 -2],[ 2 -2 0 4 4 2 0]] |
| Primitive based matrix | [[ 0 3 2 2 -2 -2 -3],[-3 0 0 -1 -2 -4 -2],[-2 0 0 -1 -1 -2 -1],[-2 1 1 0 -3 -4 -3],[ 2 2 1 3 0 0 -1],[ 2 4 2 4 0 0 -2],[ 3 2 1 3 1 2 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-3,-2,-2,2,2,3,0,1,2,4,2,1,1,2,1,3,4,3,0,1,2] |
| Phi over symmetry | [-3,-2,-2,2,2,3,-1,0,2,4,4,0,0,2,1,1,3,3,-1,0,1] |
| Phi of -K | [-3,-2,-2,2,2,3,-1,0,2,4,4,0,0,2,1,1,3,3,-1,0,1] |
| Phi of K* | [-3,-2,-2,2,2,3,0,1,1,3,4,1,0,1,2,2,3,4,0,-1,0] |
| Phi of -K* | [-3,-2,-2,2,2,3,1,2,1,3,2,0,1,3,2,2,4,4,-1,0,1] |
| Symmetry type of based matrix | c |
| u-polynomial | 0 |
| Normalized Jones-Krushkal polynomial | 11z+23 |
| Enhanced Jones-Krushkal polynomial | -2w^3z+13w^2z+23w |
| Inner characteristic polynomial | t^6+71t^4+36t^2 |
| Outer characteristic polynomial | t^7+105t^5+108t^3 |
| Flat arrow polynomial | 4*K1**3 - 8*K1**2 - 4*K1*K2 - K1 + 4*K2 + K3 + 5 |
| 2-strand cable arrow polynomial | -64*K1**4*K2**2 + 224*K1**4*K2 - 736*K1**4 + 32*K1**3*K2*K3 + 224*K1**2*K2**3 - 1440*K1**2*K2**2 + 2400*K1**2*K2 - 256*K1**2*K3**2 - 32*K1**2*K4**2 - 2032*K1**2 + 96*K1*K2**3*K3 + 1960*K1*K2*K3 + 448*K1*K3*K4 + 80*K1*K4*K5 + 8*K1*K5*K6 - 32*K2**6 + 32*K2**4*K4 - 368*K2**4 - 160*K2**2*K3**2 - 16*K2**2*K4**2 + 376*K2**2*K4 - 1454*K2**2 + 128*K2*K3*K5 + 16*K2*K4*K6 - 808*K3**2 - 324*K4**2 - 72*K5**2 - 10*K6**2 + 1778 |
| Genus of based matrix | 0 |
| Fillings of based matrix | [[{3, 6}, {2, 5}, {1, 4}]] |
| If K is slice | True |