Ranks in the family of hyperelliptic Jacobians of y2 = x5 + ax II
type: Item
instance of: scholarly article
title: Ranks in the family of hyperelliptic Jacobians of y2 = x5 + ax II
zbMATH Open document ID: 1497.11159
DOI: 10.1142/S1793042122500439
author: Tomasz Jȩdrzejak
published in: International Journal of Number Theory
publication date: 2022-06-03T00:00:00Z
Mathematics Subject Classification ID: 11G10
Mathematics Subject Classification ID: 11G30
Mathematics Subject Classification ID: 11G20
Mathematics Subject Classification ID: 11G25
zbMATH DE Number: 7536472
zbMATH Keywords: descent
zbMATH Keywords: hyperelliptic curve
zbMATH Keywords: Jacobian variety
zbMATH Keywords: Selmer group
zbMATH Keywords: rank
describes a project that uses: Magma
MaRDI profile type: Publication
Wikidata QID: Q114071922
cites work: The Magma algebra system. I: The user language
cites work: Q3310753
cites work: Effective Chabauty
cites work: Cycles of quadratic polynomials and rational points on a genus-2 curve
cites work: Q3999066
cites work: Characterization of the torsion of the Jacobians of two families of hyperelliptic curves
cites work: On the torsion of the Jacobians of the hyperelliptic curves $y^{2}=x^{n}+a$ and $y^{2}=x(x^{n}+a)$
cites work: Ranks in the family of hyperelliptic Jacobians of \(y^2=x^5+ax\)
cites work: Characterization of the torsion of the Jacobian of y2=x5+Ax and some applications
cites work: Pure quartic number fields whose class numbers are even.
cites work: 2-descent on the Jacobians of hyperelliptic curves
cites work: Computing a Selmer group of a Jacobian using functions on the curve
cites work: Implementing 2-descent for Jacobians of hyperelliptic curves
cites work: On the arithmetic of the curves o y2 = xℓ + A and their Jacobians
cites work: On the arithmetic of the curves \(y^2=x^l+A\). II
full work available at URL: s1793042122500439
OpenAlex ID: W3210149937
Recommended article: Ranks in the family of hyperelliptic Jacobians of \(y^2=x^5+ax\)
Recommended article: 2-descent on the Jacobians of hyperelliptic curves
Recommended article: Q2949509
Recommended article: On the Jacobian of a family of hyperelliptic curves
Recommended article: The rank of hyperelliptic Jacobians in families of quadratic twists
Recommended article: An Explicit Theory of Heights
Recommended article: Rank and bias in families of hyperelliptic curves via Nagao's conjecture
Recommended article: Constructing distinct curves with isomorphic Jacobians
Recommended article: On the torsion problem in Jacobians of curves of genus 2 over the rational number field
Recommended article: Q3561460
description: scientific article; zbMATH DE number 7536472