Let E be an elliptic curve defined over Q. We study the relationship between the torsion subgroup E(Q)tors and the torsion subgroup E(K)tors, where K is a cubic number field. In particular, we study… (More)

Let E be an elliptic curve defined over Q. We study the relationship between the torsion subgroup E(Q)tors and the torsion subgroup E(K)tors, where K is a quadratic number field.

Let E be an elliptic curve defined over Q and let G = E(Q)tors be the associated torsion group. In a previous paper, the authors studied, for a given G, which possible groups G ≤ H could appear such… (More)

We look for elliptic curves featuring rational points whose coordinates form two arithmetic progressions, one for each coordinate. A constructive method for creating such curves is shown, for lengths… (More)

and we consider two equations related by such a change of variables to represent the same curve (equivalently, we will deal with elliptic curves up to so-called Weierstrass changes of variables).… (More)

We find a tight relationship between the torsion subgroup and the image of the mod 2 Galois representation associated to an elliptic curve defined over the rationals. This is shown using some… (More)

In this paper we study the Kummer extensions of a power series field K = k((X1, ...,Xr)), where k is an algebraically closed field of arbitrary characteristic. The main result is that these… (More)

In this paper, the possible time invariant system equivalents to periodic ones, either in continuous-time or discretized form are considered. First, the well known Floquet-Lyapunov theorem and his… (More)