  We extend our method to compute division polynomials of Jacobians of curves
over Q to curves over Q(t), in view of computing mod ell Galois representations
occurring in the \'etale cohomology of surfaces over Q. Although the division
polynomials which we obtain are unfortunately too complicated to achieve this
last goal, we still obtain explicit families of Galois representations over
P^1_Q, and we study their degeneration at places of bad reduction of the
corresponding curve.
