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arXiv · 2106.09950

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

Davide Lombardo·Sebastiano Tronto
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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 $E(\mathbb Q)$.

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Davide Lombardo, Sebastiano Tronto. 2021-06-18. Some uniform bounds for elliptic curves over $\mathbb Q$. https://doi.org/10.2140/pjm.2022.320.133

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