Neighborhood of the supersingular elliptic curve isogeny graph at $j=0$ and $1728$

Songsong Li; Yi Ouyang; Zheng Xu

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arXiv · 1905.00244

Neighborhood of the supersingular elliptic curve isogeny graph at $j=0$ and $1728$

Songsong Li·Yi Ouyang·Zheng Xu

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Abstract

We describe the neighborhood of the vertex $[E_0]$ (resp. $[E_{1728}]$) in the $\ell$-isogeny graph $\mathcal{G}_\ell(\mathbb{F}_{p^2}, -2p)$ of supersingular elliptic curves over the finite field $\mathbb{F}_{p^2}$ when $p>3\ell^2$ (resp. $p>4\ell^2$) with $E_0: y^2=x^3+1$ (resp. $E_{1728}: y^2=x^3+x$) supersingular.

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BibTeX RIS

Songsong Li, Yi Ouyang, Zheng Xu. 2019-05-01. Neighborhood of the supersingular elliptic curve isogeny graph at $j=0$ and $1728$. https://arxiv.org/abs/1905.00244

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