Generalized division polynomials

@article{Satoh2004GeneralizedDP,
  title={Generalized division polynomials},
  author={Takakazu Satoh},
  journal={Mathematica Scandinavica},
  year={2004},
  volume={94},
  pages={161-184}
}
Let $E$ be an elliptic curve with complex multiplication by the ring $O_{F}$ of integers of an imaginary quadratic field $F$. We give an explicit condition on $\alpha\in O_{F}$ so that there exists a rational function $\psi_{\alpha}$ satisfying $\div\psi_{\alpha}=\sum_{P\in\mathrm{Ker}[\alpha]}[P] - N_{F /Q}(\alpha)[{\mathcal{O}}]$ where $[\alpha ]$ is the multiplication by $\alpha$ map. We give an algorithm to compute $\psi_{\alpha}$ based on recurrence formulas among these functions. We prove… Expand
On Degrees of Polynomial Interpolations Related to Elliptic Curve Cryptography
On the computation of generalized division polynomials
Prime power terms in elliptic divisibility sequences

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Computing division polynomials
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