Results 1 to 10 of about 2,036 (63)
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 +2 more
doaj +2 more sources
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
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
Rank zero elliptic curves induced by rational Diophantine triples [PDF]
, 2020 Rational Diophantine triples, i.e. rationals a,b,c with the property that ab+1, ac+1, bc+1 are perfect squares, are often used in construction of elliptic curves with high rank. In this paper, we consider the opposite problem and ask how small can be the
Dujella, Andrej, Mikić, Miljen
core +3 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
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
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
Different approach on elliptic curves mathematical models study and their applications
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2022 In a research project in which a group of mathematical researchers is involved, it was necessary to create a system of nonlinear equations defined over a particular nonsupersingular elliptic space.
Alsaedi Ramzi +2 more
doaj +1 more source
Conductor and discriminant of Picard curves
Journal of the London Mathematical Society, Volume 102, Issue 1, Page 368-404, August 2020., 2020 Abstract We describe normal forms and minimal models of Picard curves, discussing various arithmetic aspects of these. We determine all so‐called special Picard curves over Q with good reduction outside 2 and 3, and use this to determine the smallest possible conductor a special Picard curve may have.
Irene I. Bouw +3 more
wiley +1 more source
Torsion subgroups of rational Mordell curves over some families of number fields
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2022 Mordell curves over a number field K are elliptic curves of the form y2 = x3 + c, where c ∈ K \ {0}. Let p ≥ 5 be a prime number, K a number field such that [K : ℚ] ∈ {2p, 3p}.
Gužvić Tomislav, Roy Bidisha
doaj +1 more source