| Min(phi) over symmetries of the knot is: [-3,-2,0,1,2,2,0,2,1,2,3,2,1,2,2,1,1,1,0,0,-1] |
| Flat knots (up to 7 crossings) with same phi are :['6.783'] |
| Arrow polynomial of the knot is: -10*K1**2 - 2*K1*K2 + K1 + 5*K2 + K3 + 6 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.574', '6.593', '6.604', '6.649', '6.650', '6.673', '6.690', '6.783', '6.973', '6.985', '6.1033', '6.1035'] |
| Outer characteristic polynomial of the knot is: t^7+57t^5+53t^3+4t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.783'] |
| 2-strand cable arrow polynomial of the knot is: -64*K1**4*K2**2 + 224*K1**4*K2 - 976*K1**4 + 160*K1**3*K2*K3 - 96*K1**3*K3 + 64*K1**2*K2**2*K4 - 1760*K1**2*K2**2 - 128*K1**2*K2*K4 + 3552*K1**2*K2 - 240*K1**2*K3**2 - 32*K1**2*K4**2 - 2652*K1**2 - 416*K1*K2**2*K3 - 32*K1*K2**2*K5 - 64*K1*K2*K3*K4 + 2816*K1*K2*K3 + 608*K1*K3*K4 + 80*K1*K4*K5 - 200*K2**4 - 48*K2**2*K3**2 - 8*K2**2*K4**2 + 584*K2**2*K4 - 2206*K2**2 + 96*K2*K3*K5 + 8*K2*K4*K6 - 1040*K3**2 - 382*K4**2 - 52*K5**2 - 2*K6**2 + 2204 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.783'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.16498', 'vk6.16589', 'vk6.18105', 'vk6.18441', 'vk6.22925', 'vk6.23020', 'vk6.23483', 'vk6.23820', 'vk6.24556', 'vk6.24973', 'vk6.35005', 'vk6.35628', 'vk6.36687', 'vk6.37109', 'vk6.39464', 'vk6.41663', 'vk6.42463', 'vk6.42574', 'vk6.43967', 'vk6.44282', 'vk6.46052', 'vk6.47718', 'vk6.54741', 'vk6.54836', 'vk6.56205', 'vk6.57462', 'vk6.59201', 'vk6.59264', 'vk6.59649', 'vk6.59995', 'vk6.60804', 'vk6.62137', 'vk6.64810', 'vk6.65045', 'vk6.65555', 'vk6.65865', 'vk6.68045', 'vk6.68108', 'vk6.68637', 'vk6.68850'] |
| 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 | O1O2O3O4U3O5U6U1U4O6U2U5 |
| R3 orbit | {'O1O2O3O4U3O5U2U6U4U1O6U5', 'O1O2O3O4U3O5U6U1U4O6U2U5'} |
| R3 orbit length | 2 |
| Gauss code of -K | O1O2O3O4U5U3O6U1U4U6O5U2 |
| Gauss code of K* | O1O2O3U1O4O5U2U4U6U3O6U5 |
| Gauss code of -K* | O1O2O3U4O5U1U5U6U2O4O6U3 |
| 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 0 -1 2 3 -2],[ 2 0 1 0 2 2 1],[ 0 -1 0 -1 2 2 -1],[ 1 0 1 0 1 1 0],[-2 -2 -2 -1 0 0 -2],[-3 -2 -2 -1 0 0 -3],[ 2 -1 1 0 2 3 0]] |
| Primitive based matrix | [[ 0 3 2 0 -1 -2 -2],[-3 0 0 -2 -1 -2 -3],[-2 0 0 -2 -1 -2 -2],[ 0 2 2 0 -1 -1 -1],[ 1 1 1 1 0 0 0],[ 2 2 2 1 0 0 1],[ 2 3 2 1 0 -1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-3,-2,0,1,2,2,0,2,1,2,3,2,1,2,2,1,1,1,0,0,-1] |
| Phi over symmetry | [-3,-2,0,1,2,2,0,2,1,2,3,2,1,2,2,1,1,1,0,0,-1] |
| Phi of -K | [-2,-2,-1,0,2,3,-1,1,1,2,3,1,1,2,2,0,2,3,0,1,1] |
| Phi of K* | [-3,-2,0,1,2,2,1,1,3,2,3,0,2,2,2,0,1,1,1,1,-1] |
| Phi of -K* | [-2,-2,-1,0,2,3,-1,0,1,2,3,0,1,2,2,1,1,1,2,2,0] |
| Symmetry type of based matrix | c |
| u-polynomial | -t^3+t^2+t |
| Normalized Jones-Krushkal polynomial | 13z+27 |
| Enhanced Jones-Krushkal polynomial | 13w^2z+27w |
| Inner characteristic polynomial | t^6+35t^4+24t^2+1 |
| Outer characteristic polynomial | t^7+57t^5+53t^3+4t |
| Flat arrow polynomial | -10*K1**2 - 2*K1*K2 + K1 + 5*K2 + K3 + 6 |
| 2-strand cable arrow polynomial | -64*K1**4*K2**2 + 224*K1**4*K2 - 976*K1**4 + 160*K1**3*K2*K3 - 96*K1**3*K3 + 64*K1**2*K2**2*K4 - 1760*K1**2*K2**2 - 128*K1**2*K2*K4 + 3552*K1**2*K2 - 240*K1**2*K3**2 - 32*K1**2*K4**2 - 2652*K1**2 - 416*K1*K2**2*K3 - 32*K1*K2**2*K5 - 64*K1*K2*K3*K4 + 2816*K1*K2*K3 + 608*K1*K3*K4 + 80*K1*K4*K5 - 200*K2**4 - 48*K2**2*K3**2 - 8*K2**2*K4**2 + 584*K2**2*K4 - 2206*K2**2 + 96*K2*K3*K5 + 8*K2*K4*K6 - 1040*K3**2 - 382*K4**2 - 52*K5**2 - 2*K6**2 + 2204 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{2, 6}, {4, 5}, {1, 3}], [{2, 6}, {4, 5}, {3}, {1}], [{5, 6}, {2, 4}, {1, 3}]] |
| If K is slice | False |