Points of order l of the Jacobian of special curves of genus 2.

Let J be the Jacobian of a curve C of genus 2, defined over Q. Let p be a prime number. Assume that the reduction of the Neron model of J over Q(p) is an extension of an elliptic: curve by a torus. We denote by an algebraic closure of Q: the Galois group Gal((Q) over bar/Q) acts on the l-division points of J. We denote by rho epsilon the associated representation. Let q Le a prime number where J has good reduction such that the Galois group, over Q of the characteristic polynomial of the Frobenius endomorphism associated to q is the dihedral group with 8 elements (this implies that J is absolutely simple). Their an infinite set of prime numbers can be found such that the image of pi is GSp(4, F-l). Two exemples will be given at the end of this article.