Guanju Xiao

activity

20192024

most citedConstructing Cycles in Isogeny Graphs of Supersingular Elliptic Curves

6 citations · 8 across the 6 of their papers we have counts for

collaborators

6 papers

math.NT2024★ 1 cited

Endomorphism Rings of Supersingular Elliptic Curves and Ternary Quadratic Forms

Guanju Xiao, Zijian Zhou, Longjiang Qu

Let $c < 3 p /16$ be a prime or $c = 1$ . Let $E$ be a $Z [- c p]$ -oriented supersingular elliptic curve defined over $F_{p^{2}}$ . There exists a $c$ -isogeny from $E$ …

math.NT2023★ 1 cited

Oriented Supersingular Elliptic Curves and Eichler Orders

Guanju Xiao, Zijian Zhou, Longjiang Qu

Let $p > 3$ be a prime and $E$ be a supersingular elliptic curve defined over $F_{p^{2}}$ . Let $c$ be a prime with $c < 3 p /16$ and $G$ be a subgroup of $E [c]$ of order $c$ . Th…

math.NT2022

The Endomorphism Rings of Supersingular Elliptic Curves over $F_{p}$ and the Binary Quadratic Forms

Guanju Xiao, Zijian Zhou, Yingpu Deng +1

It is well known that there is a one-to-one correspondence between supersingular $j$ -invariants up to the action of $Gal (F_{p^{2}} / F_{p})$ and type classes of…

math.NT2021

Supersingular $j$ -invariants and the Class Number of $Q (- p)$

Guanju Xiao, Lixia Luo, Yingpu Deng

For a prime $p > 3$ , let $D$ be the discriminant of an imaginary quadratic order with $∣ D ∣ < \frac{4}{3} p$ . We research the solutions of the class polynomial $H_{D} (X)$ mo…

math.NT2020

On two problems about isogenies of elliptic curves over finite fields

Lixia Luo, Guanju Xiao, Yingpu Deng

Isogenies occur throughout the theory of elliptic curves. Recently, the cryptographic protocols based on isogenies are considered as candidates of quantum-resistant cryptographic p…

math.NT2019★ 6 cited

Constructing Cycles in Isogeny Graphs of Supersingular Elliptic Curves