Results 11 to 20 of about 568 (60)

Groups of generalized G‐type and applications to torsion subgroups of rational elliptic curves over infinite extensions of Q

Transactions of the London Mathematical Society, 2019
Recently, there has been much interest in studying the torsion subgroups of elliptic curves base‐extended to infinite extensions of Q. In this paper, given a finite group G, we study what happens with the torsion of an elliptic curve E over Q when ...
Harris B. Daniels, Maarten Derickx, Jeffrey Hatley   +2 more
doaj   +2 more sources

Non‐vanishing theorems for central L‐values of some elliptic curves with complex multiplication

Proceedings of the London Mathematical Society, Volume 121, Issue 6, Page 1531-1578, December 2020., 2020
Abstract The paper uses Iwasawa theory at the prime p=2 to prove non‐vanishing theorems for the value at s=1 of the complex L‐series of certain quadratic twists of the Gross family of elliptic curves with complex multiplication by the field K=Q(−q), where q is any prime ≡7mod8.
John Coates, Yongxiong Li
wiley   +1 more source

Models of hyperelliptic curves with tame potentially semistable reduction

Transactions of the London Mathematical Society, Volume 7, Issue 1, Page 49-95, December 2020., 2020
Abstract Let C be a hyperelliptic curve y2=f(x) over a discretely valued field K. The p‐adic distances between the roots of f(x) can be described by a completely combinatorial object known as the cluster picture. We show that the cluster picture of C, along with the leading coefficient of f and the action of Gal(K¯/K) on the roots of f, completely ...
Omri Faraggi, Sarah Nowell
wiley   +1 more source

L‐equivalence for degree five elliptic curves, elliptic fibrations and K3 surfaces

Bulletin of the London Mathematical Society, Volume 52, Issue 2, Page 395-409, April 2020., 2020
Abstract We construct non‐trivial L‐equivalence between curves of genus one and degree five, and between elliptic surfaces of multisection index five. These results give the first examples of L‐equivalence for curves (necessarily over non‐algebraically closed fields) and provide a new bit of evidence for the conjectural relationship between L ...
Evgeny Shinder, Ziyu Zhang
wiley   +1 more source

The most efficient indifferentiable hashing to elliptic curves of j-invariant 1728

Journal of Mathematical Cryptology, 2022
This article makes an important contribution to solving the long-standing problem of whether all elliptic curves can be equipped with a hash function (indifferentiable from a random oracle) whose running time amounts to one exponentiation in the basic ...
Koshelev Dmitrii
doaj   +1 more source

Constructing Cycles in Isogeny Graphs of Supersingular Elliptic Curves

Journal of Mathematical Cryptology, 2021
Loops and cycles play an important role in computing endomorphism rings of supersingular elliptic curves and related cryptosystems. For a supersingular elliptic curve E defined over 𝔽p2, if an imaginary quadratic order O can be embedded in End(E) and a ...
Xiao Guanju, Luo Lixia, Deng Yingpu
doaj   +1 more source

Orienting supersingular isogeny graphs

Journal of Mathematical Cryptology, 2020
We introduce a category of 𝓞-oriented supersingular elliptic curves and derive properties of the associated oriented and nonoriented ℓ-isogeny supersingular isogeny graphs.
Colò Leonardo, Kohel David
doaj   +1 more source

A classification of isogeny‐torsion graphs of Q‐isogeny classes of elliptic curves

Transactions of the London Mathematical Society, 2021
Let E be a Q‐isogeny class of elliptic curves defined over Q. The isogeny graph associated to E is a graph which has a vertex for each elliptic curve in the Q‐isogeny class E, and an edge for each cyclic Q‐isogeny of prime degree between elliptic curves ...
Garen Chiloyan, Álvaro Lozano‐Robledo
doaj   +1 more source

Maps from Feigin and Odesskii's elliptic algebras to twisted homogeneous coordinate rings

Forum of Mathematics, Sigma, 2021
The elliptic algebras in the title are connected graded $\mathbb {C}$-algebras, denoted $Q_{n,k}(E,\tau )$, depending on a pair of relatively prime integers $n>k\ge 1$, an elliptic curve E and a point $\tau \in E$.
Alex Chirvasitu, Ryo Kanda, S. Paul Smith   +2 more
doaj   +1 more source

On the non-idealness of cyclotomic families of pairing-friendly elliptic curves

Journal of Mathematical Cryptology, 2014
Let k=2mpn$k=2^mp^n$ for an odd prime p and integers m ≥ 0 and n ≥ 0. We obtain lower bounds for the ρ-values of cyclotomic families of pairing-friendly elliptic curves with embedding degree k and r(x)=Φk(x)$r(x)=\Phi _k(x)$.
Sha Min
doaj   +1 more source