Let $E/\mathbb{Q}$ be an elliptic curve, and let $k_1, k_2$ be square-free integers. Can anything be said about the related elliptic curves 

$$\displaystyle E/\mathbb{Q}, E^{(k_1)}/\mathbb{Q}, E^{(k_2)}/\mathbb{Q}, E^{(k_1 k_2)}/\mathbb{Q}?$$

Here $E^{(d)}$ is the quadratic twist of $E$ by $d$. If $E$ has the short Weierstrass equation 

$$\displaystyle E: y^2 = x^3 + Ax + B, A, B \in \mathbb{Z}$$

then $E^{(d)}$ has the short Weierstrass equation

$$\displaystyle E^{(d)}: dy^2 = x^3 + Ax + B.$$

In particular, let $r(E)$ denote the algebraic rank of $E$ and $r_{\text{an}}(E)$ denote the analytic rank. Are there any relations between the integers 

$$\displaystyle r(E), r(E^{(k_1)}), r(E^{(k_2)}), r(E^{(k_1 k_2)})$$

or 

$$\displaystyle r_{\text{an}}(E), r_{\text{an}}(E^{(k_1)}), r_{\text{an}}(E^{(k_2)}), r_{\text{an}}(E^{(k_1 k_2)})?$$