| Min(phi) over symmetries of the knot is: [-2,-1,0,1,1,1,-1,0,1,2,2,1,0,0,1,1,1,0,0,0,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.1756'] |
| Arrow polynomial of the knot is: -2*K1**2 - 4*K1*K2 + 2*K1 + K2 + 2*K3 + 2 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.120', '6.213', '6.216', '6.320', '6.322', '6.615', '6.617', '6.891', '6.951', '6.955', '6.1001', '6.1012', '6.1022', '6.1043', '6.1047', '6.1063', '6.1074', '6.1249', '6.1544', '6.1546', '6.1555', '6.1573', '6.1574', '6.1585', '6.1756', '6.1757', '6.1762', '6.1802', '6.1803', '6.1824', '6.1881', '6.1935'] |
| Outer characteristic polynomial of the knot is: t^7+32t^5+71t^3+11t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1756'] |
| 2-strand cable arrow polynomial of the knot is: -2128*K1**4 + 224*K1**3*K2*K3 + 64*K1**3*K3*K4 - 1056*K1**3*K3 + 96*K1**2*K2**2*K4 - 1648*K1**2*K2**2 - 640*K1**2*K2*K4 + 5168*K1**2*K2 - 816*K1**2*K3**2 - 128*K1**2*K3*K5 - 176*K1**2*K4**2 - 3300*K1**2 - 160*K1*K2**2*K3 - 64*K1*K2**2*K5 - 256*K1*K2*K3*K4 + 4376*K1*K2*K3 + 1584*K1*K3*K4 + 464*K1*K4*K5 - 200*K2**4 - 16*K2**2*K4**2 + 928*K2**2*K4 - 2900*K2**2 + 328*K2*K3*K5 + 32*K2*K4*K6 - 1672*K3**2 - 886*K4**2 - 260*K5**2 - 12*K6**2 + 3052 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1756'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.13386', 'vk6.13471', 'vk6.13662', 'vk6.13768', 'vk6.14201', 'vk6.14446', 'vk6.15673', 'vk6.16125', 'vk6.16764', 'vk6.16778', 'vk6.16881', 'vk6.19048', 'vk6.19311', 'vk6.19604', 'vk6.23187', 'vk6.23260', 'vk6.25661', 'vk6.26501', 'vk6.33141', 'vk6.33196', 'vk6.33297', 'vk6.35174', 'vk6.35201', 'vk6.37758', 'vk6.42669', 'vk6.42684', 'vk6.42780', 'vk6.44739', 'vk6.53562', 'vk6.53695', 'vk6.54971', 'vk6.64612'] |
| 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 | O1O2O3U4U5O4O6U1U6O5U3U2 |
| R3 orbit | {'O1O2O3U4U5O4O6U1U6O5U3U2'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U2U1O4U5U3O5O6U4U6 |
| Gauss code of K* | O1O2U3O4O5U1U5U4O6O3U6U2 |
| Gauss code of -K* | O1O2U3O4O5U4U6O3O6U2U1U5 |
| 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 0 1],[ 2 0 2 1 2 2 1],[-1 -2 0 0 -2 0 0],[-1 -1 0 0 -2 0 0],[ 1 -2 2 2 0 0 1],[ 0 -2 0 0 0 0 1],[-1 -1 0 0 -1 -1 0]] |
| Primitive based matrix | [[ 0 1 1 1 0 -1 -2],[-1 0 0 0 0 -2 -1],[-1 0 0 0 0 -2 -2],[-1 0 0 0 -1 -1 -1],[ 0 0 0 1 0 0 -2],[ 1 2 2 1 0 0 -2],[ 2 1 2 1 2 2 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-1,-1,-1,0,1,2,0,0,0,2,1,0,0,2,2,1,1,1,0,2,2] |
| Phi over symmetry | [-2,-1,0,1,1,1,-1,0,1,2,2,1,0,0,1,1,1,0,0,0,0] |
| Phi of -K | [-2,-1,0,1,1,1,-1,0,1,2,2,1,0,0,1,1,1,0,0,0,0] |
| Phi of K* | [-1,-1,-1,0,1,2,0,0,0,1,2,0,1,0,1,1,0,2,1,0,-1] |
| Phi of -K* | [-2,-1,0,1,1,1,2,2,1,1,2,0,1,2,2,1,0,0,0,0,0] |
| Symmetry type of based matrix | c |
| u-polynomial | t^2-2t |
| Normalized Jones-Krushkal polynomial | 4z^2+17z+19 |
| Enhanced Jones-Krushkal polynomial | -4w^4z^2+8w^3z^2-4w^3z+21w^2z+19w |
| Inner characteristic polynomial | t^6+24t^4+50t^2+4 |
| Outer characteristic polynomial | t^7+32t^5+71t^3+11t |
| Flat arrow polynomial | -2*K1**2 - 4*K1*K2 + 2*K1 + K2 + 2*K3 + 2 |
| 2-strand cable arrow polynomial | -2128*K1**4 + 224*K1**3*K2*K3 + 64*K1**3*K3*K4 - 1056*K1**3*K3 + 96*K1**2*K2**2*K4 - 1648*K1**2*K2**2 - 640*K1**2*K2*K4 + 5168*K1**2*K2 - 816*K1**2*K3**2 - 128*K1**2*K3*K5 - 176*K1**2*K4**2 - 3300*K1**2 - 160*K1*K2**2*K3 - 64*K1*K2**2*K5 - 256*K1*K2*K3*K4 + 4376*K1*K2*K3 + 1584*K1*K3*K4 + 464*K1*K4*K5 - 200*K2**4 - 16*K2**2*K4**2 + 928*K2**2*K4 - 2900*K2**2 + 328*K2*K3*K5 + 32*K2*K4*K6 - 1672*K3**2 - 886*K4**2 - 260*K5**2 - 12*K6**2 + 3052 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {2, 5}, {3, 4}], [{2, 6}, {1, 5}, {3, 4}], [{4, 6}, {1, 5}, {2, 3}], [{4, 6}, {2, 5}, {1, 3}], [{4, 6}, {3, 5}, {1, 2}], [{5, 6}, {3, 4}, {1, 2}]] |
| If K is slice | False |