Abstract : Let π: X → C be a relatively minimal genus one fibration and assume that R 1 π∗
OX
is locally free. Let b : eX
→ X be a blow-up at a smooth point x ∈π− 1 (y) . We will show that
the order of non-ordinary point y ∈C is equal to the length of the higher direct image of the
cokernel of the relative Frobenius morphism of π◦ b at y.