Rational points on quadratic elliptic surfaces

DOI10.1007/s40879-022-00577-xOpenAlexW4292756376MaRDI QIDQ2097303

Mohammad Sadek

Publication date: 11 November 2022

Published in: European Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2207.00114

zbMATH Keywords

elliptic curvesMordell-Weil rankelliptic surfacesNagao's conjecture

Mathematics Subject Classification ID

Arithmetic ground fields for curves (14H25) [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)]

Cites Work

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• On the rank of an elliptic surface
• An example of elliptic curve over \(\mathbb{Q}\) with rank \(\geq 20\)
• An example of elliptic curve over \(\mathbb{Q}\) with rank \(> 21\)
• An example of elliptic curve over \(\mathbb{Q}(T)\) with rank \(\geq 13\)
• \(\mathbb{Q} (T)\)-rank elliptic curves and certain limit coming from the local points
• Constructing one-parameter families of elliptic curves with moderate rank
• Lower-Order Biases in Elliptic Curve Fourier Coefficients in Families
• Une courbe elliptique définie sur ℚ de rang ≥ 22
• Étude expérimentale du rang de families de courbeselliptiques sur Q
• Quadratic families of elliptic curves and unirationality of degree 1 conic bundles

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