Corpus ID: 14941436

On the surjectivity of mod ell representations associated to elliptic curves

@article{Zywina2015OnTS,
  title={On the surjectivity of mod ell representations associated to elliptic curves},
  author={D. Zywina},
  journal={arXiv: Number Theory},
  year={2015}
}
  • D. Zywina
  • Published 2015
  • Mathematics
  • arXiv: Number Theory
  • Let $E$ be an elliptic curve over the rationals that does not have complex multiplication. For each prime $\ell$, the action of the absolute Galois group on the $\ell$-torsion points of $E$ can be given in terms of a Galois representation $\rho_{E,\ell}\colon G \to GL_2(\mathbb{F}_\ell)$, where $G$ is the absolute Galois group of the rationals. An important theorem of Serre says that $\rho_{E,\ell}$ is surjective for all sufficiently large $\ell$. In this paper, we describe an algorithm based… CONTINUE READING

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