| Résume | The irreducibility and transversality of a curve are crucial conditions in many theorems in the context of anomalous intersections. However, given a family of curves in EN for E an elliptic curve, it is not easy to decide weather they are irreducible or transverse. I will present some criteria and some examples. I will also explain how such properties can be used, together with some height bounds, to determine the K-rational points on some families of curves. |
