Some uniform bounds for elliptic curves over $\mathbb{Q}$

Abstract

We give explicit uniform bounds for several quantities relevant to the study of Galois representations attached to elliptic curves $E/\mathbb{Q}$. We consider in particular the subgroup of scalars in the image of Galois, the first Galois cohomology group with values in the torsion of $E$, and the Kummer extensions generated by points of infinite order in $E(\mathbb{Q})$.

Comments are welcome!

References in corpus (1)

• Borne uniforme pour les homothéties dans l'image de Galois associée aux courbes elliptiques

Cited by in corpus (2)

• $\ell$-adic images of Galois for elliptic curves over $\mathbb{Q}$
• Torsion points on isogenous abelian varieties