Results 21 to 30 of about 568 (60)
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
Selmer groups and torsion zero cycles on the selfproduct of a semistable elliptic curve
Documenta Mathematica, 1997 In this paper we extend the niteness result on the p-primary torsion subgroup in the Chow group of zero cycles on the selfproduct of a semistable elliptic curve obtained in joint work with S. Saito to primes p dividing the conductor.
A. Langer
semanticscholar +1 more source
On elliptic curves of prime power conductor over imaginary quadratic fields with class number 1
Proceedings of the London Mathematical Society, Volume 118, Issue 5, Page 1245-1276, May 2019., 2019 Abstract The main result of this paper is to extend from Q to each of the nine imaginary quadratic fields of class number 1 a result of [Serre, Duke Math. J. 54 (1987) 179–230] and [Mestre–Oesterlé, J. reine. angew. Math. 400 (1989) 173–184], namely that if E is an elliptic curve of prime conductor, then either E or a 2‐, 3‐ or 5‐isogenous curve has ...
John Cremona, Ariel Pacetti
wiley +1 more source
On the Mahler measure of hyperelliptic families
, 2016 We prove Boyd's "unexpected coincidence" of the Mahler measures for two families of two-variate polynomials defining curves of genus 2. We further equate the same measures to the Mahler measures of polynomials $y^3-y+x^3-x+kxy$ whose zero loci define ...
Bertin, Marie José, Zudilin, Wadim
core +2 more sources
Efficient computation of pairings on Jacobi quartic elliptic curves
Journal of Mathematical Cryptology, 2014 This paper proposes the computation of the Tate pairing, Ate pairing and its variations on the special Jacobi quartic elliptic curve Y2=dX4+Z4$Y^{2}=dX^{4}+Z^{4}$.
Duquesne Sylvain +2 more
doaj +1 more source
Tight closure and plus closure for cones over elliptic curves [PDF]
, 2005 We characterize the tight closure of graded primary ideals in a homogeneous coordinate ring over an elliptic curve by numerical conditions and we show that it is in positive characteristic the same as the plus closure.Comment: Some minor ...
Brenner, Holger
core +2 more sources
On simultaneous arithmetic progressions on elliptic curves [PDF]
, 2006 In this paper we study elliptic curves which have a number of points whose coordinates are in arithmetic progression. We first motivate this diophantine problem, prove some results, provide a number of interesting examples and, finally point out open ...
Garcia-Selfa, I., Tornero, J. M.
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, 1992 The propagation differential for bosonic strings on a complex torus with three symmetric punctures is investigated. We study deformation aspects between two point and three point differentials as well as the behaviour of the corresponding Krichever ...
A. Hurwitz +14 more
core +4 more sources
Edwards Curves and Gaussian Hypergeometric Series [PDF]
, 2015 Let $E$ be an elliptic curve described by either an Edwards model or a twisted Edwards model over $\mathbb{F}_p$, namely, $E$ is defined by one of the following equations $x^2+y^2=a^2(1+x^2y^2),\, a^5-a\not\equiv 0$ mod $p$, or, $ax^2+y^2=1+dx^2y^2,\,ad ...
El-Sissi, Nermine, Sadek, Mohammad
core +3 more sources
Constructing elliptic curve isogenies in quantum subexponential time
Journal of Mathematical Cryptology, 2014 Given two ordinary elliptic curves over a finite field having the same cardinality and endomorphism ring, it is known that the curves admit a nonzero isogeny between them, but finding such an isogeny is believed to be computationally difficult.
Childs Andrew +2 more
doaj +1 more source