Modular curves over number fields and ECM (Q2100579)

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scientific article; zbMATH DE number 7622898

Language	Label	Description	Also known as
English	Modular curves over number fields and ECM	scientific article; zbMATH DE number 7622898

Statements

scholarly article

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Modular curves over number fields and ECM (English)

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Research in Number Theory

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publication date

24 November 2022

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zbMATH Keywords

elliptic curves

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Cunningham numbers

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François Morain

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describes a project that uses

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MaRDI profile type

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full work available at URL

https://doi.org/10.1007/s40993-022-00394-x

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High rank elliptic curves with prescribed torsion group over quadratic fields

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Elliptic Curves and Primality Proving

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Finding Suitable Curves for the Elliptic Curve Method of Factorization

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Note on taking square-roots modulo N

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Finding ECM-friendly curves through a study of Galois properties

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A classification of ECM-friendly families of elliptic curves using modular curves

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ECM using Edwards curves

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Twisted Hessian Curves

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CRITÈRES D'IRRÉDUCTIBILITÉ POUR LES REPRÉSENTATIONS DES COURBES ELLIPTIQUES

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Ranks of Elliptic Curves with Prescribed Torsion over Number Fields

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New Families of ECM Curves for Cunningham Numbers

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Factorizations of 𝑏ⁿ±1, 𝑏=2, 3, 5, 6, 7, 10, 11, 12 Up to High Powers

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Sequences of numbers generated by addition in formal groups and new primality and factorization tests

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\(\mathbb{Q}\)-curves over odd degree number fields

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Torsion of elliptic curves over cyclic cubic fields

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Torsion subgroups of elliptic curves over quintic and sextic number fields

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Diophantine triples and construction of high-rank elliptic curves over \(\mathbb{Q}\) with three nontrivial 2-torsion points

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Elliptic curves with torsion groups \(\mathbb{Z}/8\mathbb{Z}\) and \(\mathbb{Z}/2\mathbb{Z} \times \mathbb{Z}/6\mathbb{Z}\)

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Elliptic curves with large torsion and positive rank over number fields of small degree and ECM factorization

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Parametrizations for Families of ECM-Friendly Curves

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Families of elliptic curves over cubic number fields with prescribed torsion subgroups

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Families of elliptic curves over quartic number fields with prescribed torsion subgroups

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Torsion points on elliptic curves and \(q\)-coefficients of modular forms

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Torsion points on elliptic curves defined over quadratic fields

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Construction of high-rank elliptic curves with a non-trivial rational point of order 2

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On the rank of elliptic curves with three rational points of order 2. II

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Addition law structure of elliptic curves

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Universal Bounds on the Torsion of Elliptic Curves

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Courbes elliptiques de rang ≥ 5 sur Q(t) avec un groupe de torsion isomorphe à Z/2Z × Z/2Z

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Families of elliptic curves of high rank with nontrivial torsion group over Q

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Elliptic Curves of High Rank with Nontrivial Torsion Group over Q

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On the rank of elliptic curves with a torsion group isomorphic to \(\mathbb{Z}/5\mathbb{Z}\)

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Rank of elliptic curves with nontrivial torsion group

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Rang de familles de courbes elliptiques

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Factoring integers with elliptic curves

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Bounds for the torsion of elliptic curves over number fields

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Speeding the Pollard and Elliptic Curve Methods of Factorization

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Implementing the asymptotically fast version of the elliptic curve primality proving algorithm

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Construction of high-rank elliptic curves with a nontrivial torsion point

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Bornes effectives pour la torsion des courbes elliptiques sur les corps de nombres

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Structure de torsion des courbes elliptiques sur les corps quadratiques

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Explicit determination of nontrivial torsion structures of elliptic curves over quadratic number fields

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Torsion groups of elliptic curves over quadratic fields $\mathbb{Q}(\sqrt{d})$, $0 \lt d \lt 100$

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On the cyclic torsion of elliptic curves over cubic number fields

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On the cyclic torsion of elliptic curves over cubic number fields. II

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A p + 1 Method of Factoring

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Algorithmic Number Theory

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Identifiers

zbMATH Open document ID

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Mathematics Subject Classification ID

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zbMATH DE Number

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10.1007/S40993-022-00394-X

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Sitelinks

Mathematics(1 entry)

mardi Publication:2100579

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