Guanju Xiao

activity

20202024

collaborators

3 papers

math.NT2024

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.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…

Endomorphism Rings of Supersingular Elliptic Curves and Ternary Quadratic Forms

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

On two problems about isogenies of elliptic curves over finite fields

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