Ranks in the family of hyperelliptic Jacobians of y2 = x5 + ax II

DOI10.1142/S1793042122500439zbMath1497.11159OpenAlexW3210149937WikidataQ114071922 ScholiaQ114071922MaRDI QIDQ5863777

Tomasz Jędrzejak

Publication date: 3 June 2022

Published in: International Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s1793042122500439

zbMATH Keywords

hyperelliptic curverankJacobian varietydescentSelmer group

Mathematics Subject Classification ID

Abelian varieties of dimension (> 1) (11G10) Curves over finite and local fields (11G20) [https://portal.mardi4nfdi.de/w/index.php?title=+Special%3ASearch&search=%22Curves+of+arbitrary+genus+or+genus+%28%0D%0Ae+1%29+over+global+fields%22&go=Go Curves of arbitrary genus or genus ( e 1) over global fields (11G30)] Varieties over finite and local fields (11G25)

Uses Software

• Magma

Cites Work

• Effective Chabauty
• The Magma algebra system. I: The user language
• Cycles of quadratic polynomials and rational points on a genus-2 curve
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• Ranks in the family of hyperelliptic Jacobians of \(y^2=x^5+ax\)
• Implementing 2-descent for Jacobians of hyperelliptic curves
• Characterization of the torsion of the Jacobians of two families of hyperelliptic curves
• Characterization of the torsion of the Jacobian of y²=x⁵+Ax and some applications
• On the torsion of the Jacobians of the hyperelliptic curves $y^{2}=x^{n}+a$ and $y^{2}=x(x^{n}+a)$
• Pure quartic number fields whose class numbers are even.
• On the arithmetic of the curves o y2 = xℓ + A and their Jacobians
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