Zobrazeno 1 - 10
of 9 618
pro vyhledávání: '"Isogeny"'
Autor:
Perrin, Derek, Voloch, José Felipe
We study $\ell$-isogeny graphs of ordinary elliptic curves defined over $\mathbb{F}_q$ with an added level structure. Given an integer $N$ coprime to $p$ and $\ell,$ we look at the graphs obtained by adding $\Gamma_0(N),$ $\Gamma_1(N),$ and $\Gamma(N
Externí odkaz:
http://arxiv.org/abs/2411.02732
In this paper, we introduce the study of minimal torsion curves within a fixed geometric isogeny class. For a $\overline{\mathbb{Q}}$-isogeny class $\mathcal{E}$ of elliptic curves and $N \in \mathbb{Z}^+$, we wish to determine the least degree of a
Externí odkaz:
http://arxiv.org/abs/2407.14322
E-governance is a two-way protocol through which one can use government services, share data and request information. It refers to the use of communication and information technologies to provide government services to public in an efficient and fast
Externí odkaz:
http://arxiv.org/abs/2407.13318
Autor:
Bourdon, Abbey, Genao, Tyler
In 1996, Merel showed there exists a function $B\colon \mathbb{Z}^+\rightarrow \mathbb{Z}^+$ such that for any elliptic curve $E/F$ defined over a number field of degree $d$, one has the torsion group bound $\# E(F)[\textrm{tors}]\leq B(d)$. Based on
Externí odkaz:
http://arxiv.org/abs/2409.08214
Autor:
Ferrigno, Luca
Let $E_{\lambda}$ be the Legendre family of elliptic curves with equation $Y^2=X(X-1)(X-\lambda)$. Given a curve $\mathcal{C}$, satisfying a condition on the degrees of some of its coordinates and parametrizing $m$ points $P_1, \ldots, P_m \in E_{\la
Externí odkaz:
http://arxiv.org/abs/2409.01408
Autor:
Hashimoto, Yuji, Nuida, Koji
It is known that any isogeny graph consisting of ordinary elliptic curves over $\mathbb{F}_q$ with $q = p$ or $p^2$ has a special structure, called a volcano graph. We have a bound $h < \log_2 \sqrt{4q}$ of a height $h$ of the $2$-volcano graph. In t
Externí odkaz:
http://arxiv.org/abs/2409.00505
Autor:
Barrios, Alexander, Cullinan, John
Let $\ell$ be an odd prime, and suppose $E$ is an elliptic curve defined over the rational numbers $\mathbb{Q}$. If $E$ has an $\ell$-torsion point, then there has been significant work done on characterizing the $\ell$-divisibility of the global Tam
Externí odkaz:
http://arxiv.org/abs/2408.03419
Autor:
Kieffer, Jean
We describe how isogenies between principally polarized abelian surfaces (PPAS) with real multiplication (RM) can be decomposed into elementary isogeny types. This leads to a strategy for enumerating the isogeny class of a given PPAS with RM. This no
Externí odkaz:
http://arxiv.org/abs/2405.19820
Autor:
Bhatnagar, Tejasi
We prove a lower bound for the size of the isogeny class of a simple abelian variety over a finite field with commutative endomorphism ring in the extended Lubin-Tate case. Moreover, based on the expected size of the isogeny classes in the Newton str
Externí odkaz:
http://arxiv.org/abs/2405.02758
Autor:
Ghosh, Sohan, Ray, Jishnu
Consider a function field $K$ with characteristic $p>0$. We investigate the $\Lambda$-module structure of the Mordell-Weil group of an abelian variety over $\mathbb{Z}_p$-extensions of $K$, generalizing results due to Lee. Next, we study the algebrai
Externí odkaz:
http://arxiv.org/abs/2406.03201