  L. Szpiro and T. Tucker recently proved that under mild conditions, the
valuation of the minimal discriminant of an elliptic curve with semistable
reduction over a discrete valuation ring can be expressed in terms of
intersections between n-torsion and 2-torsion, where n tends to infinity. The
argument of Szpiro and Tucker is geometric in nature. We give a proof based on
the arithmetic of division polynomials, and generalize the result to the case
of hyperelliptic curves.
