Analytic ranks of elliptic curves over number fields

Let E be an elliptic curve over Q. Then, we show that the average analytic rank of E over cyclic extensions of degree l over Q with l a prime not equal to 2, is at most 2+rQ(E), where rQ(E) is the analytic rank of the elliptic curve E over Q. This bound is independent of the degree l Also, we also obtain some average analytic rank results over Sd-fields