| Min(phi) over symmetries of the knot is: [-3,-2,-1,1,2,3,-1,1,1,4,4,0,0,2,1,0,2,2,-1,0,1] |
| Flat knots (up to 7 crossings) with same phi are :['6.812'] |
| Arrow polynomial of the knot is: 4*K1**3 - 4*K1**2 - 4*K1*K2 - K1 + 2*K2 + K3 + 3 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.209', '6.231', '6.391', '6.419', '6.600', '6.661', '6.744', '6.812', '6.826', '6.1114', '6.1125', '6.1202', '6.1275', '6.1292', '6.1305', '6.1322', '6.1365', '6.1481', '6.1483', '6.1497', '6.1543', '6.1549', '6.1572', '6.1577', '6.1580', '6.1594', '6.1641', '6.1658', '6.1683', '6.1753', '6.1830', '6.1907', '6.1928'] |
| Outer characteristic polynomial of the knot is: t^7+94t^5+126t^3+9t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.812'] |
| 2-strand cable arrow polynomial of the knot is: -64*K1**4 - 64*K1**3*K3 - 192*K1**2*K2**4 + 448*K1**2*K2**3 + 128*K1**2*K2**2*K4 - 5200*K1**2*K2**2 - 416*K1**2*K2*K4 + 6784*K1**2*K2 - 64*K1**2*K3**2 - 128*K1**2*K4**2 - 5816*K1**2 + 192*K1*K2**3*K3 - 480*K1*K2**2*K3 - 96*K1*K2**2*K5 + 5776*K1*K2*K3 + 824*K1*K3*K4 + 136*K1*K4*K5 - 32*K2**6 + 32*K2**4*K4 - 784*K2**4 - 48*K2**2*K3**2 - 16*K2**2*K4**2 + 1296*K2**2*K4 - 3902*K2**2 + 56*K2*K3*K5 + 16*K2*K4*K6 + 8*K3**2*K6 - 1728*K3**2 - 696*K4**2 - 56*K5**2 - 10*K6**2 + 4094 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.812'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.11080', 'vk6.11160', 'vk6.12244', 'vk6.12353', 'vk6.18326', 'vk6.18663', 'vk6.24758', 'vk6.25215', 'vk6.30657', 'vk6.30750', 'vk6.31883', 'vk6.31953', 'vk6.36940', 'vk6.37405', 'vk6.44133', 'vk6.44455', 'vk6.51869', 'vk6.51916', 'vk6.52734', 'vk6.52843', 'vk6.56114', 'vk6.56335', 'vk6.60629', 'vk6.60964', 'vk6.63523', 'vk6.63569', 'vk6.64003', 'vk6.64049', 'vk6.65760', 'vk6.66022', 'vk6.68766', 'vk6.68974'] |
| 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 | O1O2O3O4U1O5U3U6U5U4O6U2 |
| R3 orbit | {'O1O2O3O4U1O5U3U6U5U4O6U2'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U3O5U1U6U5U2O6U4 |
| Gauss code of K* | O1O2O3O4U2O5U6U5U1U4O6U3 |
| Gauss code of -K* | O1O2O3O4U2O5U1U4U6U5O6U3 |
| 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 1 -1 3 2 -2],[ 3 0 3 1 2 1 2],[-1 -3 0 -2 2 2 -3],[ 1 -1 2 0 2 1 -1],[-3 -2 -2 -2 0 0 -4],[-2 -1 -2 -1 0 0 -2],[ 2 -2 3 1 4 2 0]] |
| Primitive based matrix | [[ 0 3 2 1 -1 -2 -3],[-3 0 0 -2 -2 -4 -2],[-2 0 0 -2 -1 -2 -1],[-1 2 2 0 -2 -3 -3],[ 1 2 1 2 0 -1 -1],[ 2 4 2 3 1 0 -2],[ 3 2 1 3 1 2 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-3,-2,-1,1,2,3,0,2,2,4,2,2,1,2,1,2,3,3,1,1,2] |
| Phi over symmetry | [-3,-2,-1,1,2,3,-1,1,1,4,4,0,0,2,1,0,2,2,-1,0,1] |
| Phi of -K | [-3,-2,-1,1,2,3,-1,1,1,4,4,0,0,2,1,0,2,2,-1,0,1] |
| Phi of K* | [-3,-2,-1,1,2,3,1,0,2,1,4,-1,2,2,4,0,0,1,0,1,-1] |
| Phi of -K* | [-3,-2,-1,1,2,3,2,1,3,1,2,1,3,2,4,2,1,2,2,2,0] |
| Symmetry type of based matrix | c |
| u-polynomial | 0 |
| Normalized Jones-Krushkal polynomial | 7z^2+26z+25 |
| Enhanced Jones-Krushkal polynomial | 7w^3z^2+26w^2z+25w |
| Inner characteristic polynomial | t^6+66t^4+76t^2+4 |
| Outer characteristic polynomial | t^7+94t^5+126t^3+9t |
| Flat arrow polynomial | 4*K1**3 - 4*K1**2 - 4*K1*K2 - K1 + 2*K2 + K3 + 3 |
| 2-strand cable arrow polynomial | -64*K1**4 - 64*K1**3*K3 - 192*K1**2*K2**4 + 448*K1**2*K2**3 + 128*K1**2*K2**2*K4 - 5200*K1**2*K2**2 - 416*K1**2*K2*K4 + 6784*K1**2*K2 - 64*K1**2*K3**2 - 128*K1**2*K4**2 - 5816*K1**2 + 192*K1*K2**3*K3 - 480*K1*K2**2*K3 - 96*K1*K2**2*K5 + 5776*K1*K2*K3 + 824*K1*K3*K4 + 136*K1*K4*K5 - 32*K2**6 + 32*K2**4*K4 - 784*K2**4 - 48*K2**2*K3**2 - 16*K2**2*K4**2 + 1296*K2**2*K4 - 3902*K2**2 + 56*K2*K3*K5 + 16*K2*K4*K6 + 8*K3**2*K6 - 1728*K3**2 - 696*K4**2 - 56*K5**2 - 10*K6**2 + 4094 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{5, 6}, {1, 4}, {2, 3}]] |
| If K is slice | False |