Heegner Points on Cartan Non-split Curves

@article{Kohen2016HeegnerPO,
  title={Heegner Points on Cartan Non-split Curves},
  author={Daniela Kohen and Ariel Pacetti},
  journal={Canadian Journal of Mathematics},
  year={2016},
  volume={68},
  pages={422 - 444}
}
Abstract Let $E/\mathbb{Q}$ be an elliptic curve of conductor $N$ , and let $K$ be an imaginary quadratic field such that the root number of $E/K$ is −1. Let $O$ be an order in $K$ and assume that there exists an odd prime $p$ such that ${{p}^{2}}\,\parallel \,N$ , and $p$ is inert in $O$ . Although there are no Heegner points on ${{X}_{0}}(N)$ attached to $O$ , in this article we construct such points on Cartan non-split curves. In order to do that, we give a method to compute Fourier… 

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