Legendrian Knot Atlas

Here are the Legendrian knots representing knot type 8_12 = m(8_12) with (tb, r) =(-5,0) :

Grid Diagram
(tb, r)
L = -L?
L = μ(L)?
L = -μ(L)?
Ruling invariant
Linearized Contact Homology
Transverse Invariant
(-5,0)
✗?
✗?
✓
1
[2*t^-1 + 3*t]
[[0, 0, 0, 0], 0]
(-5,0)
✗?
✗?
✓
1
[t^-3 + t^-1 + 2*t + t^3]
[[0, 0, 0, 0], 0]
(-5,0)
✗?
✓
✗?
1
[2*t^-1 + 3*t]
[[0, 0, 0, 0], 0]
(-5,0)
✓
✓
✓
1
[2*t^-1 + 3*t]
[[0, 0, 0, 0], 0]