On \(K\)-derived quartics

DOI10.1016/J.JNT.2016.04.024zbMath1396.11055OpenAlexW2417297140MaRDI QIDQ301442

Benjamin Carrillo, Andrew Bremner

Publication date: 30 June 2016

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

Full work available at URL: https://doi.org/10.1016/j.jnt.2016.04.024

zbMATH Keywords

elliptic curvesquadratic fieldsderived quarticslinear factors

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) [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)] Cubic and quartic Diophantine equations (11D25) Higher degree equations; Fermat's equation (11D41)

Uses Software

• Magma

Cites Work

• The Magma algebra system. I: The user language
• When Newton met Diophantus: a study of rational-derived polynomials and their extension to quadratic fields.
• A diophantine problem from calculus
• On \(\mathbb Q\)-derived polynomials
• On elliptic modular surfaces
• ON ℚ-DERIVED POLYNOMIALS
• Polynomials All of Whose Derivatives Have Integer Roots
• On rational-derived quartics

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