[Physics] Solenoidal electric field

Question

In electrostatic electric field in a system is always irrotational ∇×E=0. And divergence of electric field is non zero ∇.E=ρ/ε but in some cases divergence of electric field is also zero ∇.E=0 such as in case of dipole I had calculated and got that ∇.E=0 for a dipole
So in case of this dipole divergence and curl both are zero
So what does it mean when a vector fieLd do not diverge and not rotational at all
So what kind of nature it has??
∇×E=0 , ∇.E=0.
So it means the electric field is both solenoidal and irrotational ,but how can these two conditions satisfy simultaneously? If a vector field is solenoidal then it has to rotate ,must have some curliness

But in pic of a dipole I can see that the electric field is bending or rotating

Then what does it mean about zero curl (∇×E=0)?
I can see the electric field is rotational

Answer 1

div E does not vanish everywhere for the dipole, you should get delta-functions in the points where there are charges.